Unit 8 Test

Select the equation for the following cubic function and describe the transformation from the parent function.

•  $f\left(x\right)=-\left(x-3\right)^3-1$  

•  $f\left(x\right)=\left(x+3\right)^3+1$  

•  $f\left(x\right)=\sqrt{x+3}+1$  

What transformations has the function undergone?

• reflect over y, vertical compress by 2, right 5, up 1
• reflect over x, horizontal compression by 2, left 5, up 1
• reflect over x, vertical stretch by 2, right 5, up 1
• reflect over y, horizontal stretch by -2, right 5, up 1

Tags

CCSS.HSF.BF.B.3

Identify the Inverse of  $y=x^{3\ }-5$  

•  $f\left(x\right)^{-1}=^3\sqrt{x+5}$  

•  $f\left(x\right)^{-1}=^3\sqrt{x-5}$  

•  $f\left(x\right)^{-1}=x^3-5$  

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

Solve for  $x$  
 $5=^3\sqrt{x+1}+1$  

•  $x=-63$  

•  $x=63$  

•  $x=1$  

•  $x=5$  

 $f\left(x\right)=\sqrt{x-5}+1$  Identify the inverse of the following equations.

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

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

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

Solve for x given that  $-2\ =\ ^3\sqrt{x-4}+1$  

• The value of x is 4.

• The value of x is 3.
  

• The value of x is -23.

• The value of x is 6.
  

Tags

CCSS.HSA.REI.A.2

Solve for x given  $\frac{1}{3}\left(x\ ^{\frac{3}{2}}-5\right)=40$  

• The value of x is 45.
  

• The value of x is 25.
  

• The value of x is 35.
  

• The value of x is 30.
  

Given  $f\left(x\right)\ =\ 4\cdot\left(x-3\right)^2+1$  , Identify all the transformations of f(x).

• The function was vertically stretched by a factor of 4, translated right by 3 units, and translated up by 1 unit.
  

• The function was vertically compressed by a factor of 4, translated left by 3 units, and translated down by 1 unit.

• The function was horizontally stretched by a factor of 4, translated right by 3 units, and translated up by 1 unit.

• The function was horizontally compressed by a factor of 4, translated left by 3 units, and translated down by 1 unit.

Given  $g\left(x\right)\ =\ 2\cdot\left(^3\sqrt{x+1}\right)-3$  , find the vertex of the equation.

• The vertex of the equation is (1 , -3).
  

• The vertex of the equation is (-1 , 3).

• The vertex of the equation is (1 , 3).

• The vertex of the equation is (-1 , -3).

Tags

CCSS.HSF-IF.C.7B

• 1.44

• 27

• 7.35

• 9

Tags

CCSS.8.EE.A.2