Vertical Dilations of Linear Functions

Given the function $f\left(x\right)=x$ , what conclusions can you make about  $f\left(x\right)$  and  $4f\left(x\right)$ ? SELECT ALL THAT APPLY.

• The function  $f\left(x\right)$  has a greater rate of change than  $4f\left(x\right)$  .

• The y-intercepts are the same.

•  $f\left(4\right)<4f\left(4\right)$  

• The function  $4f\left(x\right)$  is a translation down 4 units of the function $f\left(x\right)$  .

When applying a vertical dilation to a linear function, which statements below are true? SELECT ALL THAT APPLY.

• The slope remains the same.

• The slope changes.

• The lines will be parallel.

• The lines will not be parallel.

Given the function $f\left(x\right)=x$ , what conclusions can you make about  $f\left(x\right)$  and  $-f\left(x\right)$ ? SELECT ALL THAT APPLY.

• The function  $f\left(x\right)$  has a greater rate of change than  $-f\left(x\right)$  .

• The y-intercepts are different.

• The functions are reflections about the x-axis.

• The functions have the same average rate of change.

Given the function $f\left(x\right)=x$ , what conclusions can you make about  $f\left(x\right)$  and  $0.5f\left(x\right)$ ? SELECT ALL THAT APPLY.

• The distance between the y-intercepts is 0.5.

• The function $f\left(x\right)$ is twice as steep as  $0.5f\left(x\right)$  .

• The functions  $0.5f\left(x\right)$  is linear.

• Both functions pass through the origin.

When applying a vertical translation (shift up or down) to a linear function, which statements below are true? SELECT ALL THAT APPLY.

• The slope remains the same and the y-intercept changes.

• The slope changes and the y-intercept remains the same.

• The lines will be parallel.

• The lines will not be parallel.

Given the function $f\left(x\right)=x$ , what conclusions can you make about  $f\left(x\right)$  and  $f\left(x\right)+5$ ? SELECT ALL THAT APPLY.

•  $f\left(x\right)+5$ has a greater y-intercept than  $f\left(x\right)$  .

• The rate of change of $f\left(x\right)$ is less than  $f\left(x\right)+5$  .

• The lines are parallel.

• Both functions pass through the origin.