Graphing and Transforming Cubic Functions

What are the transformations?
y=(x-2)³+4

• Horz shift right 2      Vert shift up 4
• Horz shift left 2    Vert shift down 4
• Horz shift right 2      Vert shift down 4
• Horz shift left 2      Vert shift up 4

Describe the transformation of the graph  y = -2(x + 5)³ 

• Shrink by 2, Reflected over y-axis, Right 5
• Stretch by 2, Reflected over x-axis, Left 5
• Stretch by 2, Reflected over x-axis, Right 5
• Shrink by 2, reflected over y-axis, Left 5

Describe the transformation of the graph  
y = ½x³

• Vertical compression by 1/2
• Horizontal compression by 1/2
• Vertical stretch by 2
• Horizontal stretch by 2

Describe the transformation of the graph  y = -2(x + 5)³ 

• Shrink by 2, Reflected over y-axis, Right 5
• Stretch by 2, Reflected over x-axis, Left 5
• Stretch by 2, Reflected over x-axis, Right 5
• Shrink by 2, reflected over y-axis, Left 5

The graph shows the function f(x)=x³ in blue and another function g(x) in red.  Which could be the equation for g(x)?

• A.  g(x) = -x³
• B.  g(x) = x³ - 1
• C.  g(x) = (x + 1)³
• D.  g(x) = (x - 1)³

What is the y-intercept of the following cubic function?

• (1, 0)
• (0, 2)
• (-1, 0)
• (2, 0)

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

Describe the transformation of the graph  y = - ½(x + 4)³ - 1

• Left 4 and Down 1
• Reflected x-axis, Down 1, Left 4, Shrink by 1/2
• Reflected x-axis, Down 1, Left 4, Stretch by 1/2
• Reflected x-axis, Up 1, Right 4, Shrink by 1/2

What kind of function is represented by the graph?

• Cubic Root Function
• Cubic Function
• Polynomial Function
• Square Root Function

• A
• B
• C
• D