Finite Math Examples

Find the x and y Intercepts y=4*(1/2)^(x-2)-2
Step 1
Find the x-intercepts.
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Step 1.1
To find the x-intercept(s), substitute in for and solve for .
Step 1.2
Solve the equation.
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Step 1.2.1
Rewrite the equation as .
Step 1.2.2
Simplify each term.
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Step 1.2.2.1
Apply the product rule to .
Step 1.2.2.2
One to any power is one.
Step 1.2.2.3
Combine and .
Step 1.2.3
Add to both sides of the equation.
Step 1.2.4
Move to the numerator using the negative exponent rule .
Step 1.2.5
Rewrite as .
Step 1.2.6
Use the power rule to combine exponents.
Step 1.2.7
Create equivalent expressions in the equation that all have equal bases.
Step 1.2.8
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
Step 1.2.9
Solve for .
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Step 1.2.9.1
Simplify .
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Step 1.2.9.1.1
Simplify each term.
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Step 1.2.9.1.1.1
Apply the distributive property.
Step 1.2.9.1.1.2
Multiply by .
Step 1.2.9.1.2
Add and .
Step 1.2.9.2
Move all terms not containing to the right side of the equation.
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Step 1.2.9.2.1
Subtract from both sides of the equation.
Step 1.2.9.2.2
Subtract from .
Step 1.2.9.3
Divide each term in by and simplify.
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Step 1.2.9.3.1
Divide each term in by .
Step 1.2.9.3.2
Simplify the left side.
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Step 1.2.9.3.2.1
Dividing two negative values results in a positive value.
Step 1.2.9.3.2.2
Divide by .
Step 1.2.9.3.3
Simplify the right side.
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Step 1.2.9.3.3.1
Divide by .
Step 1.3
x-intercept(s) in point form.
x-intercept(s):
x-intercept(s):
Step 2
Find the y-intercepts.
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Step 2.1
To find the y-intercept(s), substitute in for and solve for .
Step 2.2
Solve the equation.
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Step 2.2.1
Remove parentheses.
Step 2.2.2
Remove parentheses.
Step 2.2.3
Simplify .
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Step 2.2.3.1
Simplify each term.
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Step 2.2.3.1.1
Subtract from .
Step 2.2.3.1.2
Change the sign of the exponent by rewriting the base as its reciprocal.
Step 2.2.3.1.3
Raise to the power of .
Step 2.2.3.1.4
Multiply by .
Step 2.2.3.2
Subtract from .
Step 2.3
y-intercept(s) in point form.
y-intercept(s):
y-intercept(s):
Step 3
List the intersections.
x-intercept(s):
y-intercept(s):
Step 4