Pre-Algebra Examples

Graph f(x) = square root of 7x-3
Step 1
Find the domain for so that a list of values can be picked to find a list of points, which will help graphing the radical.
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Step 1.1
Set the radicand in greater than or equal to to find where the expression is defined.
Step 1.2
Solve for .
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Step 1.2.1
Add to both sides of the inequality.
Step 1.2.2
Divide each term in by and simplify.
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Step 1.2.2.1
Divide each term in by .
Step 1.2.2.2
Simplify the left side.
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Step 1.2.2.2.1
Cancel the common factor of .
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Step 1.2.2.2.1.1
Cancel the common factor.
Step 1.2.2.2.1.2
Divide by .
Step 1.3
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Interval Notation:
Set-Builder Notation:
Step 2
To find the radical expression end point, substitute the value , which is the least value in the domain, into .
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Step 2.1
Replace the variable with in the expression.
Step 2.2
Simplify the result.
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Step 2.2.1
Cancel the common factor of .
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Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Rewrite the expression.
Step 2.2.2
Simplify the expression.
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Step 2.2.2.1
Subtract from .
Step 2.2.2.2
Rewrite as .
Step 2.2.2.3
Pull terms out from under the radical, assuming positive real numbers.
Step 2.2.3
The final answer is .
Step 3
The radical expression end point is .
Step 4
Select a few values from the domain. It would be more useful to select the values so that they are next to the value of the radical expression end point.
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Step 4.1
Substitute the value into . In this case, the point is .
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Step 4.1.1
Replace the variable with in the expression.
Step 4.1.2
Simplify the result.
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Step 4.1.2.1
Multiply by .
Step 4.1.2.2
Subtract from .
Step 4.1.2.3
Rewrite as .
Step 4.1.2.4
Pull terms out from under the radical, assuming positive real numbers.
Step 4.1.2.5
The final answer is .
Step 4.2
Substitute the value into . In this case, the point is .
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Step 4.2.1
Replace the variable with in the expression.
Step 4.2.2
Simplify the result.
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Step 4.2.2.1
Multiply by .
Step 4.2.2.2
Subtract from .
Step 4.2.2.3
The final answer is .
Step 4.3
The square root can be graphed using the points around the vertex
Step 5