Unit 3: Mid-Chapter Review

Unit 3:

Mid-Chapter Review

Generating the INVERSE with tables is as easy as switching the x and y values to create a new table.

Multiple Choice

Generate the inverse of the function represented in the table.

Multiple Choice

Generate the inverse of the function represented in the table.

Multiple Select

Determine the x-intercept and y-intercept of the original function using the given graph and then identify the intercepts of the inverse.

[Click the graph to enlarge then CHOOSE TWO ANSWERS]

• Original

  x-intercept (3, 0)

  y-intercept (0, -3)

• Original

  x-intercept (0, 3)

  y-intercept (-3, 0)

• Inverse

  x-intercept (-3, 0)

  y-intercept (0, 3)

• Inverse

  x-intercept (0, -3)

  y-intercept (3, 0)

Multiple Choice

The graph of the function

 $f\left(x\right)=\left(x-2\right)^3-5$  is shown.

If the point (4, 3) is on the graph of f(x), give the point on the graph of the inverse that corresponds.

• (-4, -3)

• (3, 4)

• (-3, -4)

• no point would correspond

Multiple Choice

Generate  $f^{-1}\left(x\right)$  , the equation of the inverse of the function given.

 $f\left(x\right)=\frac{1}{2}x+5$  

•  $f^{-1}\left(x\right)=\frac{1}{2}y-5$  

•  $f^{-1}\left(x\right)=2\left(x-5\right)$  

•  $f^{-1}\left(x\right)=-\frac{1}{2}x-5$  

Multiple Choice

Generate    $f^{-1}\left(x\right)$   , the equation of the inverse of the function given.

 $f\left(x\right)=\frac{1}{4}\left(x+1\right)^2$  

•  $f^{-1}\left(x\right)=\sqrt{4x}-1$  

•  $f^{-1}\left(x\right)=-\frac{1}{4}\left(x-1\right)^2$  

•  $f^{-1}\left(x\right)=4\sqrt{x}+1$  

Inverse Functions will have x and y values that have swapped places

Multiple Select

Indicate whether or not the data in each pair of tables represent the inverse functions or relations.

[Click the picture to enlarge]

• Inverse Functions

• Not Inverse Functions

Multiple Select

Indicate whether or not the data in each pair of tables represent the inverse functions or relations.

[Click the picture to enlarge]

• Inverse Functions

• Not Inverse Functions

Verifying Inverses with GRAPHS

Corresponding points should flip the x and y values.

Example: (-8, 0) and (0, -8)

Multiple Select

Indicate whether or not the graphs represent an inverse relationship.

[Click the picture to enlarge]

• Inverses

• Not Inverses

Multiple Select

Indicate whether or not each graph represents an inverse relationship.

[Click the picture to enlarge]

• Inverses

• Not Inverses

Generating the inverse of Quadratics

Multiple Choice

Generate the square root function that is the inverse of the given quadratic function.

 $f\left(x\right)=4\left(x+3\right)^2$  

•  $f^{-1}\left(x\right)=-4\left(x-3\right)^2$  

•  $f^{-1}\left(x\right)=\sqrt{4x+3}$  

•  $f^{-1}\left(x\right)=\frac{\sqrt{x}}{2}-3$  

•  $f^{-1}\left(x\right)=2\sqrt{x}-3$  

Multiple Select

Verify whether or not  $f\left(x\right)=x^2+4$ and   $g\left(x\right)=\sqrt{x-4}$ are inverses if the domain of   $f\left(x\right)$ is restricted to   $\left\{x\ |\ x\ge0\right\}$  .

[make sure you view the video in the previous slide]

• Inverses

• Not Inverses

Endpoint of Square Root Functions

 $\left(\frac{c}{b},\ d\right)$  

Multiple Choice

Identify the endpoint of the square root function.

 $f\left(x\right)=\sqrt{x-1}+3$  

• (-1, 3)

• (1, -3)

• (-1, -3)

• (1, 3)

Multiple Choice

Identify the y-intercept of the INVERSE function.

[click the image to enlarge]

• (0, 3)

• (3, 0)

• (0, 9)

• (9, 0)

Multiple Select

Create a table that represents the inverse.

[click the image to enlarge]

• This is not the answer

• This is not the answer