Pre-Algebra Examples

Find the Function Rule table[[x,y],[-5,10],[7,-2],[0,15],[4,-5]]
Step 1
Check if the function rule is linear.
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Step 1.1
To find if the table follows a function rule, check to see if the values follow the linear form .
Step 1.2
Build a set of equations from the table such that .
Step 1.3
Calculate the values of and .
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Step 1.3.1
Rewrite the equation as .
Step 1.3.2
Replace all occurrences of with in each equation.
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Step 1.3.2.1
Replace all occurrences of in with .
Step 1.3.2.2
Simplify .
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Step 1.3.2.2.1
Simplify the left side.
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Step 1.3.2.2.1.1
Remove parentheses.
Step 1.3.2.2.2
Simplify the right side.
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Step 1.3.2.2.2.1
Move to the left of .
Step 1.3.2.3
Replace all occurrences of in with .
Step 1.3.2.4
Simplify .
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Step 1.3.2.4.1
Simplify the left side.
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Step 1.3.2.4.1.1
Remove parentheses.
Step 1.3.2.4.2
Simplify the right side.
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Step 1.3.2.4.2.1
Move to the left of .
Step 1.3.2.5
Replace all occurrences of in with .
Step 1.3.2.6
Simplify .
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Step 1.3.2.6.1
Simplify the left side.
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Step 1.3.2.6.1.1
Remove parentheses.
Step 1.3.2.6.2
Simplify the right side.
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Step 1.3.2.6.2.1
Move to the left of .
Step 1.3.3
Solve for in .
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Step 1.3.3.1
Rewrite the equation as .
Step 1.3.3.2
Move all terms not containing to the right side of the equation.
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Step 1.3.3.2.1
Subtract from both sides of the equation.
Step 1.3.3.2.2
Subtract from .
Step 1.3.3.3
Divide each term in by and simplify.
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Step 1.3.3.3.1
Divide each term in by .
Step 1.3.3.3.2
Simplify the left side.
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Step 1.3.3.3.2.1
Cancel the common factor of .
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Step 1.3.3.3.2.1.1
Cancel the common factor.
Step 1.3.3.3.2.1.2
Divide by .
Step 1.3.3.3.3
Simplify the right side.
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Step 1.3.3.3.3.1
Divide by .
Step 1.3.4
Replace all occurrences of with in each equation.
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Step 1.3.4.1
Replace all occurrences of in with .
Step 1.3.4.2
Simplify the right side.
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Step 1.3.4.2.1
Simplify .
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Step 1.3.4.2.1.1
Multiply by .
Step 1.3.4.2.1.2
Add and .
Step 1.3.4.3
Replace all occurrences of in with .
Step 1.3.4.4
Simplify the right side.
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Step 1.3.4.4.1
Simplify .
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Step 1.3.4.4.1.1
Multiply by .
Step 1.3.4.4.1.2
Add and .
Step 1.3.5
Since is not true, there is no solution.
No solution
No solution
Step 1.4
Since for the corresponding values, the function is not linear.
The function is not linear
The function is not linear
Step 2
Check if the function rule is quadratic.
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Step 2.1
To find if the table follows a function rule, check whether the function rule could follow the form .
Step 2.2
Build a set of equations from the table such that .
Step 2.3
Calculate the values of , , and .
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Step 2.3.1
Solve for in .
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Step 2.3.1.1
Rewrite the equation as .
Step 2.3.1.2
Simplify .
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Step 2.3.1.2.1
Simplify each term.
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Step 2.3.1.2.1.1
Raising to any positive power yields .
Step 2.3.1.2.1.2
Multiply by .
Step 2.3.1.2.2
Add and .
Step 2.3.2
Replace all occurrences of with in each equation.
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Step 2.3.2.1
Replace all occurrences of in with .
Step 2.3.2.2
Simplify .
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Step 2.3.2.2.1
Simplify the left side.
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Step 2.3.2.2.1.1
Remove parentheses.
Step 2.3.2.2.2
Simplify the right side.
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Step 2.3.2.2.2.1
Simplify each term.
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Step 2.3.2.2.2.1.1
Raise to the power of .
Step 2.3.2.2.2.1.2
Move to the left of .
Step 2.3.2.2.2.1.3
Move to the left of .
Step 2.3.2.3
Replace all occurrences of in with .
Step 2.3.2.4
Simplify .
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Step 2.3.2.4.1
Simplify the left side.
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Step 2.3.2.4.1.1
Remove parentheses.
Step 2.3.2.4.2
Simplify the right side.
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Step 2.3.2.4.2.1
Simplify each term.
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Step 2.3.2.4.2.1.1
Raise to the power of .
Step 2.3.2.4.2.1.2
Move to the left of .
Step 2.3.2.4.2.1.3
Move to the left of .
Step 2.3.2.5
Replace all occurrences of in with .
Step 2.3.2.6
Simplify .
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Step 2.3.2.6.1
Simplify the left side.
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Step 2.3.2.6.1.1
Remove parentheses.
Step 2.3.2.6.2
Simplify the right side.
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Step 2.3.2.6.2.1
Simplify each term.
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Step 2.3.2.6.2.1.1
Raise to the power of .
Step 2.3.2.6.2.1.2
Move to the left of .
Step 2.3.2.6.2.1.3
Move to the left of .
Step 2.3.3
Solve for in .
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Step 2.3.3.1
Rewrite the equation as .
Step 2.3.3.2
Move all terms not containing to the right side of the equation.
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Step 2.3.3.2.1
Subtract from both sides of the equation.
Step 2.3.3.2.2
Subtract from both sides of the equation.
Step 2.3.3.2.3
Subtract from .
Step 2.3.3.3
Divide each term in by and simplify.
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Step 2.3.3.3.1
Divide each term in by .
Step 2.3.3.3.2
Simplify the left side.
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Step 2.3.3.3.2.1
Cancel the common factor of .
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Step 2.3.3.3.2.1.1
Cancel the common factor.
Step 2.3.3.3.2.1.2
Divide by .
Step 2.3.3.3.3
Simplify the right side.
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Step 2.3.3.3.3.1
Simplify each term.
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Step 2.3.3.3.3.1.1
Cancel the common factor of and .
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Step 2.3.3.3.3.1.1.1
Factor out of .
Step 2.3.3.3.3.1.1.2
Cancel the common factors.
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Step 2.3.3.3.3.1.1.2.1
Factor out of .
Step 2.3.3.3.3.1.1.2.2
Cancel the common factor.
Step 2.3.3.3.3.1.1.2.3
Rewrite the expression.
Step 2.3.3.3.3.1.2
Move the negative in front of the fraction.
Step 2.3.3.3.3.1.3
Cancel the common factor of and .
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Step 2.3.3.3.3.1.3.1
Factor out of .
Step 2.3.3.3.3.1.3.2
Cancel the common factors.
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Step 2.3.3.3.3.1.3.2.1
Factor out of .
Step 2.3.3.3.3.1.3.2.2
Cancel the common factor.
Step 2.3.3.3.3.1.3.2.3
Rewrite the expression.
Step 2.3.3.3.3.1.4
Move the negative in front of the fraction.
Step 2.3.4
Replace all occurrences of with in each equation.
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Step 2.3.4.1
Replace all occurrences of in with .
Step 2.3.4.2
Simplify the right side.
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Step 2.3.4.2.1
Simplify .
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Step 2.3.4.2.1.1
Simplify each term.
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Step 2.3.4.2.1.1.1
Apply the distributive property.
Step 2.3.4.2.1.1.2
Multiply .
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Step 2.3.4.2.1.1.2.1
Multiply by .
Step 2.3.4.2.1.1.2.2
Combine and .
Step 2.3.4.2.1.1.3
Multiply .
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Step 2.3.4.2.1.1.3.1
Multiply by .
Step 2.3.4.2.1.1.3.2
Combine and .
Step 2.3.4.2.1.1.3.3
Multiply by .
Step 2.3.4.2.1.1.4
Simplify each term.
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Step 2.3.4.2.1.1.4.1
Move the negative in front of the fraction.
Step 2.3.4.2.1.1.4.2
Move the negative in front of the fraction.
Step 2.3.4.2.1.2
To write as a fraction with a common denominator, multiply by .
Step 2.3.4.2.1.3
Combine and .
Step 2.3.4.2.1.4
Combine the numerators over the common denominator.
Step 2.3.4.2.1.5
Combine the numerators over the common denominator.
Step 2.3.4.2.1.6
Multiply by .
Step 2.3.4.2.1.7
Add and .
Step 2.3.4.2.1.8
Factor out of .
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Step 2.3.4.2.1.8.1
Factor out of .
Step 2.3.4.2.1.8.2
Factor out of .
Step 2.3.4.2.1.8.3
Factor out of .
Step 2.3.4.2.1.9
To write as a fraction with a common denominator, multiply by .
Step 2.3.4.2.1.10
Simplify terms.
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Step 2.3.4.2.1.10.1
Combine and .
Step 2.3.4.2.1.10.2
Combine the numerators over the common denominator.
Step 2.3.4.2.1.11
Simplify the numerator.
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Step 2.3.4.2.1.11.1
Multiply by .
Step 2.3.4.2.1.11.2
Apply the distributive property.
Step 2.3.4.2.1.11.3
Multiply by .
Step 2.3.4.2.1.11.4
Multiply by .
Step 2.3.4.2.1.11.5
Subtract from .
Step 2.3.4.2.1.12
Simplify with factoring out.
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Step 2.3.4.2.1.12.1
Factor out of .
Step 2.3.4.2.1.12.2
Rewrite as .
Step 2.3.4.2.1.12.3
Factor out of .
Step 2.3.4.2.1.12.4
Simplify the expression.
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Step 2.3.4.2.1.12.4.1
Rewrite as .
Step 2.3.4.2.1.12.4.2
Move the negative in front of the fraction.
Step 2.3.4.3
Replace all occurrences of in with .
Step 2.3.4.4
Simplify the right side.
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Step 2.3.4.4.1
Simplify .
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Step 2.3.4.4.1.1
Simplify each term.
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Step 2.3.4.4.1.1.1
Apply the distributive property.
Step 2.3.4.4.1.1.2
Multiply .
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Step 2.3.4.4.1.1.2.1
Multiply by .
Step 2.3.4.4.1.1.2.2
Combine and .
Step 2.3.4.4.1.1.3
Multiply .
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Step 2.3.4.4.1.1.3.1
Multiply by .
Step 2.3.4.4.1.1.3.2
Combine and .
Step 2.3.4.4.1.1.3.3
Multiply by .
Step 2.3.4.4.1.1.4
Simplify each term.
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Step 2.3.4.4.1.1.4.1
Move the negative in front of the fraction.
Step 2.3.4.4.1.1.4.2
Move the negative in front of the fraction.
Step 2.3.4.4.1.2
To write as a fraction with a common denominator, multiply by .
Step 2.3.4.4.1.3
Combine and .
Step 2.3.4.4.1.4
Combine the numerators over the common denominator.
Step 2.3.4.4.1.5
Combine the numerators over the common denominator.
Step 2.3.4.4.1.6
Multiply by .
Step 2.3.4.4.1.7
Subtract from .
Step 2.3.4.4.1.8
Factor out of .
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Step 2.3.4.4.1.8.1
Factor out of .
Step 2.3.4.4.1.8.2
Factor out of .
Step 2.3.4.4.1.8.3
Factor out of .
Step 2.3.4.4.1.9
To write as a fraction with a common denominator, multiply by .
Step 2.3.4.4.1.10
Simplify terms.
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Step 2.3.4.4.1.10.1
Combine and .
Step 2.3.4.4.1.10.2
Combine the numerators over the common denominator.
Step 2.3.4.4.1.11
Simplify the numerator.
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Step 2.3.4.4.1.11.1
Factor out of .
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Step 2.3.4.4.1.11.1.1
Factor out of .
Step 2.3.4.4.1.11.1.2
Factor out of .
Step 2.3.4.4.1.11.2
Multiply by .
Step 2.3.4.4.1.11.3
Subtract from .
Step 2.3.4.4.1.12
Simplify with factoring out.
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Step 2.3.4.4.1.12.1
Factor out of .
Step 2.3.4.4.1.12.2
Rewrite as .
Step 2.3.4.4.1.12.3
Factor out of .
Step 2.3.4.4.1.12.4
Simplify the expression.
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Step 2.3.4.4.1.12.4.1
Rewrite as .
Step 2.3.4.4.1.12.4.2
Move the negative in front of the fraction.
Step 2.3.5
Solve for in .
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Step 2.3.5.1
Rewrite the equation as .
Step 2.3.5.2
Multiply both sides of the equation by .
Step 2.3.5.3
Simplify both sides of the equation.
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Step 2.3.5.3.1
Simplify the left side.
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Step 2.3.5.3.1.1
Simplify .
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Step 2.3.5.3.1.1.1
Cancel the common factor of .
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Step 2.3.5.3.1.1.1.1
Move the leading negative in into the numerator.
Step 2.3.5.3.1.1.1.2
Move the leading negative in into the numerator.
Step 2.3.5.3.1.1.1.3
Factor out of .
Step 2.3.5.3.1.1.1.4
Cancel the common factor.
Step 2.3.5.3.1.1.1.5
Rewrite the expression.
Step 2.3.5.3.1.1.2
Cancel the common factor of .
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Step 2.3.5.3.1.1.2.1
Factor out of .
Step 2.3.5.3.1.1.2.2
Cancel the common factor.
Step 2.3.5.3.1.1.2.3
Rewrite the expression.
Step 2.3.5.3.1.1.3
Multiply.
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Step 2.3.5.3.1.1.3.1
Multiply by .
Step 2.3.5.3.1.1.3.2
Multiply by .
Step 2.3.5.3.2
Simplify the right side.
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Step 2.3.5.3.2.1
Simplify .
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Step 2.3.5.3.2.1.1
Cancel the common factor of .
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Step 2.3.5.3.2.1.1.1
Move the leading negative in into the numerator.
Step 2.3.5.3.2.1.1.2
Factor out of .
Step 2.3.5.3.2.1.1.3
Cancel the common factor.
Step 2.3.5.3.2.1.1.4
Rewrite the expression.
Step 2.3.5.3.2.1.2
Multiply by .
Step 2.3.5.4
Move all terms not containing to the right side of the equation.
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Step 2.3.5.4.1
Subtract from both sides of the equation.
Step 2.3.5.4.2
Subtract from .
Step 2.3.5.5
Divide each term in by and simplify.
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Step 2.3.5.5.1
Divide each term in by .
Step 2.3.5.5.2
Simplify the left side.
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Step 2.3.5.5.2.1
Cancel the common factor of .
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Step 2.3.5.5.2.1.1
Cancel the common factor.
Step 2.3.5.5.2.1.2
Divide by .
Step 2.3.5.5.3
Simplify the right side.
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Step 2.3.5.5.3.1
Cancel the common factor of and .
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Step 2.3.5.5.3.1.1
Factor out of .
Step 2.3.5.5.3.1.2
Cancel the common factors.
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Step 2.3.5.5.3.1.2.1
Factor out of .
Step 2.3.5.5.3.1.2.2
Cancel the common factor.
Step 2.3.5.5.3.1.2.3
Rewrite the expression.
Step 2.3.5.5.3.2
Move the negative in front of the fraction.
Step 2.3.6
Replace all occurrences of with in each equation.
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Step 2.3.6.1
Replace all occurrences of in with .
Step 2.3.6.2
Simplify the right side.
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Step 2.3.6.2.1
Simplify .
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Step 2.3.6.2.1.1
Simplify the numerator.
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Step 2.3.6.2.1.1.1
Cancel the common factor of .
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Step 2.3.6.2.1.1.1.1
Move the leading negative in into the numerator.
Step 2.3.6.2.1.1.1.2
Factor out of .
Step 2.3.6.2.1.1.1.3
Cancel the common factor.
Step 2.3.6.2.1.1.1.4
Rewrite the expression.
Step 2.3.6.2.1.1.2
Multiply by .
Step 2.3.6.2.1.1.3
Add and .
Step 2.3.6.2.1.2
Simplify the expression.
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Step 2.3.6.2.1.2.1
Divide by .
Step 2.3.6.2.1.2.2
Multiply by .
Step 2.3.6.3
Replace all occurrences of in with .
Step 2.3.6.4
Simplify the right side.
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Step 2.3.6.4.1
Simplify .
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Step 2.3.6.4.1.1
Combine the numerators over the common denominator.
Step 2.3.6.4.1.2
To write as a fraction with a common denominator, multiply by .
Step 2.3.6.4.1.3
Combine and .
Step 2.3.6.4.1.4
Combine the numerators over the common denominator.
Step 2.3.6.4.1.5
Simplify the numerator.
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Step 2.3.6.4.1.5.1
Multiply by .
Step 2.3.6.4.1.5.2
Subtract from .
Step 2.3.6.4.1.6
Move the negative in front of the fraction.
Step 2.3.6.4.1.7
Multiply the numerator by the reciprocal of the denominator.
Step 2.3.6.4.1.8
Cancel the common factor of .
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Step 2.3.6.4.1.8.1
Move the leading negative in into the numerator.
Step 2.3.6.4.1.8.2
Factor out of .
Step 2.3.6.4.1.8.3
Cancel the common factor.
Step 2.3.6.4.1.8.4
Rewrite the expression.
Step 2.3.6.4.1.9
Move the negative in front of the fraction.
Step 2.3.7
Since is not true, there is no solution.
No solution
No solution
Step 2.4
Calculate the value of using each value in the table and compare this value to the given value in the table.
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Step 2.4.1
Calculate the value of such that when , , , and .
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Step 2.4.1.1
Simplify each term.
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Step 2.4.1.1.1
Raise to the power of .
Step 2.4.1.1.2
Multiply by .
Step 2.4.1.1.3
Multiply by .
Step 2.4.1.2
Simplify by adding numbers.
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Step 2.4.1.2.1
Add and .
Step 2.4.1.2.2
Add and .
Step 2.4.2
If the table has a quadratic function rule, for the corresponding value, . This check does not pass, since and . The function rule can't be quadratic.
Step 2.4.3
Since for the corresponding values, the function is not quadratic.
The function is not quadratic
The function is not quadratic
The function is not quadratic
Step 3
Check if the function rule is cubic.
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Step 3.1
To find if the table follows a function rule, check whether the function rule could follow the form .
Step 3.2
Build a set of equations from the table such that .
Step 3.3
Calculate the values of , , , and .
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Step 3.3.1
Solve for in .
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Step 3.3.1.1
Rewrite the equation as .
Step 3.3.1.2
Simplify each term.
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Step 3.3.1.2.1
Raise to the power of .
Step 3.3.1.2.2
Move to the left of .
Step 3.3.1.2.3
Raise to the power of .
Step 3.3.1.2.4
Move to the left of .
Step 3.3.1.2.5
Move to the left of .
Step 3.3.1.3
Move all terms not containing to the right side of the equation.
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Step 3.3.1.3.1
Add to both sides of the equation.
Step 3.3.1.3.2
Subtract from both sides of the equation.
Step 3.3.1.3.3
Add to both sides of the equation.
Step 3.3.2
Replace all occurrences of with in each equation.
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Step 3.3.2.1
Replace all occurrences of in with .
Step 3.3.2.2
Simplify .
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Step 3.3.2.2.1
Simplify the left side.
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Step 3.3.2.2.1.1
Remove parentheses.
Step 3.3.2.2.2
Simplify the right side.
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Step 3.3.2.2.2.1
Simplify .
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Step 3.3.2.2.2.1.1
Combine the opposite terms in .
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Step 3.3.2.2.2.1.1.1
Reorder the factors in the terms and .
Step 3.3.2.2.2.1.1.2
Add and .
Step 3.3.2.2.2.1.1.3
Add and .
Step 3.3.2.2.2.1.2
Simplify each term.
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Step 3.3.2.2.2.1.2.1
Raise to the power of .
Step 3.3.2.2.2.1.2.2
Move to the left of .
Step 3.3.2.2.2.1.2.3
Raise to the power of .
Step 3.3.2.2.2.1.2.4
Move to the left of .
Step 3.3.2.2.2.1.3
Simplify by adding terms.
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Step 3.3.2.2.2.1.3.1
Combine the opposite terms in .
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Step 3.3.2.2.2.1.3.1.1
Subtract from .
Step 3.3.2.2.2.1.3.1.2
Add and .
Step 3.3.2.2.2.1.3.2
Add and .
Step 3.3.2.3
Replace all occurrences of in with .
Step 3.3.2.4
Simplify .
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Step 3.3.2.4.1
Simplify the left side.
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Step 3.3.2.4.1.1
Remove parentheses.
Step 3.3.2.4.2
Simplify the right side.
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Step 3.3.2.4.2.1
Simplify .
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Step 3.3.2.4.2.1.1
Combine the opposite terms in .
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Step 3.3.2.4.2.1.1.1
Reorder the factors in the terms and .
Step 3.3.2.4.2.1.1.2
Add and .
Step 3.3.2.4.2.1.1.3
Add and .
Step 3.3.2.4.2.1.2
Simplify each term.
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Step 3.3.2.4.2.1.2.1
Raising to any positive power yields .
Step 3.3.2.4.2.1.2.2
Multiply by .
Step 3.3.2.4.2.1.2.3
Raise to the power of .
Step 3.3.2.4.2.1.2.4
Move to the left of .
Step 3.3.2.4.2.1.3
Combine the opposite terms in .
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Step 3.3.2.4.2.1.3.1
Add and .
Step 3.3.2.4.2.1.3.2
Subtract from .
Step 3.3.2.4.2.1.3.3
Add and .
Step 3.3.2.5
Replace all occurrences of in with .
Step 3.3.2.6
Simplify .
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Step 3.3.2.6.1
Simplify the left side.
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Step 3.3.2.6.1.1
Remove parentheses.
Step 3.3.2.6.2
Simplify the right side.
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Step 3.3.2.6.2.1
Simplify .
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Step 3.3.2.6.2.1.1
Combine the opposite terms in .
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Step 3.3.2.6.2.1.1.1
Reorder the factors in the terms and .
Step 3.3.2.6.2.1.1.2
Add and .
Step 3.3.2.6.2.1.1.3
Add and .
Step 3.3.2.6.2.1.2
Simplify each term.
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Step 3.3.2.6.2.1.2.1
Raise to the power of .
Step 3.3.2.6.2.1.2.2
Move to the left of .
Step 3.3.2.6.2.1.2.3
Raise to the power of .
Step 3.3.2.6.2.1.2.4
Move to the left of .
Step 3.3.2.6.2.1.3
Simplify by adding terms.
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Step 3.3.2.6.2.1.3.1
Combine the opposite terms in .
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Step 3.3.2.6.2.1.3.1.1
Subtract from .
Step 3.3.2.6.2.1.3.1.2
Add and .
Step 3.3.2.6.2.1.3.2
Add and .
Step 3.3.3
Solve for in .
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Step 3.3.3.1
Rewrite the equation as .
Step 3.3.3.2
Move all terms not containing to the right side of the equation.
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Step 3.3.3.2.1
Subtract from both sides of the equation.
Step 3.3.3.2.2
Subtract from .
Step 3.3.3.3
Divide each term in by and simplify.
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Step 3.3.3.3.1
Divide each term in by .
Step 3.3.3.3.2
Simplify the left side.
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Step 3.3.3.3.2.1
Cancel the common factor of .
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Step 3.3.3.3.2.1.1
Cancel the common factor.
Step 3.3.3.3.2.1.2
Divide by .
Step 3.3.3.3.3
Simplify the right side.
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Step 3.3.3.3.3.1
Cancel the common factor of and .
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Step 3.3.3.3.3.1.1
Factor out of .
Step 3.3.3.3.3.1.2
Cancel the common factors.
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Step 3.3.3.3.3.1.2.1
Factor out of .
Step 3.3.3.3.3.1.2.2
Cancel the common factor.
Step 3.3.3.3.3.1.2.3
Rewrite the expression.
Step 3.3.3.3.3.2
Move the negative in front of the fraction.
Step 3.3.4
Replace all occurrences of with in each equation.
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Step 3.3.4.1
Replace all occurrences of in with .
Step 3.3.4.2
Simplify the right side.
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Step 3.3.4.2.1
Simplify .
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Step 3.3.4.2.1.1
Simplify each term.
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Step 3.3.4.2.1.1.1
Multiply .
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Step 3.3.4.2.1.1.1.1
Multiply by .
Step 3.3.4.2.1.1.1.2
Combine and .
Step 3.3.4.2.1.1.1.3
Multiply by .
Step 3.3.4.2.1.1.2
Move the negative in front of the fraction.
Step 3.3.4.2.1.2
To write as a fraction with a common denominator, multiply by .
Step 3.3.4.2.1.3
Combine and .
Step 3.3.4.2.1.4
Combine the numerators over the common denominator.
Step 3.3.4.2.1.5
Simplify the numerator.
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Step 3.3.4.2.1.5.1
Multiply by .
Step 3.3.4.2.1.5.2
Subtract from .
Step 3.3.4.3
Replace all occurrences of in with .
Step 3.3.4.4
Simplify the right side.
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Step 3.3.4.4.1
Simplify .
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Step 3.3.4.4.1.1
Simplify each term.
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Step 3.3.4.4.1.1.1
Cancel the common factor of .
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Step 3.3.4.4.1.1.1.1
Move the leading negative in into the numerator.
Step 3.3.4.4.1.1.1.2
Factor out of .
Step 3.3.4.4.1.1.1.3
Factor out of .
Step 3.3.4.4.1.1.1.4
Cancel the common factor.
Step 3.3.4.4.1.1.1.5
Rewrite the expression.
Step 3.3.4.4.1.1.2
Combine and .
Step 3.3.4.4.1.1.3
Multiply by .
Step 3.3.4.4.1.1.4
Move the negative in front of the fraction.
Step 3.3.4.4.1.2
To write as a fraction with a common denominator, multiply by .
Step 3.3.4.4.1.3
Combine and .
Step 3.3.4.4.1.4
Combine the numerators over the common denominator.
Step 3.3.4.4.1.5
Simplify the numerator.
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Step 3.3.4.4.1.5.1
Multiply by .
Step 3.3.4.4.1.5.2
Add and .
Step 3.3.4.4.1.6
Move the negative in front of the fraction.
Step 3.3.4.5
Replace all occurrences of in with .
Step 3.3.4.6
Simplify the right side.
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Step 3.3.4.6.1
Simplify .
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Step 3.3.4.6.1.1
Simplify each term.
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Step 3.3.4.6.1.1.1
Multiply .
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Step 3.3.4.6.1.1.1.1
Multiply by .
Step 3.3.4.6.1.1.1.2
Combine and .
Step 3.3.4.6.1.1.1.3
Multiply by .
Step 3.3.4.6.1.1.2
Move the negative in front of the fraction.
Step 3.3.4.6.1.2
To write as a fraction with a common denominator, multiply by .
Step 3.3.4.6.1.3
Combine and .
Step 3.3.4.6.1.4
Combine the numerators over the common denominator.
Step 3.3.4.6.1.5
Simplify the numerator.
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Step 3.3.4.6.1.5.1
Multiply by .
Step 3.3.4.6.1.5.2
Subtract from .
Step 3.3.5
Since is not true, there is no solution.
No solution
No solution
Step 3.4
Calculate the value of using each value in the table and compare this value to the given value in the table.
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Step 3.4.1
Calculate the value of such that when , , , , and .
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Step 3.4.1.1
Simplify each term.
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Step 3.4.1.1.1
Raise to the power of .
Step 3.4.1.1.2
Multiply by .
Step 3.4.1.1.3
Raise to the power of .
Step 3.4.1.1.4
Multiply .
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Step 3.4.1.1.4.1
Multiply by .
Step 3.4.1.1.4.2
Multiply by .
Step 3.4.1.1.5
Multiply .
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Step 3.4.1.1.5.1
Multiply by .
Step 3.4.1.1.5.2
Multiply by .
Step 3.4.1.2
Simplify by adding numbers.
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Step 3.4.1.2.1
Add and .
Step 3.4.1.2.2
Add and .
Step 3.4.2
If the table has a cubic function rule, for the corresponding value, . This check does not pass, since and . The function rule can't be cubic.
Step 3.4.3
Since for the corresponding values, the function is not cubic.
The function is not cubic
The function is not cubic
The function is not cubic
Step 4
There are no values for , , , and in the equations , , and that work for every pair of and .
The table does not have a function rule that is linear, quadratic, or cubic.