Cube and Cube Root Equations

Identify the Transformations. 

• Vertical stretch by 2 and down 4
• Horizontal compression by ½ and down 4
• Vertical stretch by 2 and up 4
• Horizontal compression by ½ and right 4

What does it mean to find the inverse of a function?

• the x's and y's are switched
• the x's and y's are divided by 2
• the x's and y's are made negative
• the x's and y's are the same

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

What kind of function is represented by the graph?

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

Which of the facts is not true about the graph shown?

• The range is y ∈ ℝ
• The function has been shifted 6 units right.
• The function has been shifted up 1 unit
• The function has been vertically stretched by a factor of 2. 

  What is the equation for the red function? 

• g(x)=x³+1
• g(x)=x³-1
• g(x)=(x-1)³
• g(x)=(x+1)³

The graph of a function is shown.  What are the domain and range of this function?

• Domain: (-∞, ∞)
  Range: (-∞, 2]
• Domain: [2, ∞)
  Range: (-∞, ∞)
• Domain: (-∞, ∞)
  Range: (-∞, ∞)
• Domain: (-∞, 2]
  Range: [2, ∞)

If f(x) = x³ is changed to f(x) = - (x + 3)³ + 2, how is the graph transformed?

• 3 units right, 2 units up, reflected across the y-axis
• 3 units right, 2 units up, reflected across the x-axis
• 3 units left, 2 units up, reflected across the y-axis
• 3 units left, 2 units up, reflected across the x-axis

If f(x) = ∛(x) is reflected over the x-axis, vertically compressed by a factor of 1/4, and shifted left 9, which equation is correct?

• 1/4 ∛(x + 9)
• 1/4 ∛(x - 9)
• - 1/4 ∛(x + 9)
• - 1/4 ∛(x - 9)

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

• (1, 0)
• (0, 2)
• (-1, 0)
• (2, 0)