Parent Functions, Key Features, Transformations, Composition

Describe the transformation of the function from the Parent Function g(x)=-x^3+5

• Reflection over

  x-axis

  and

  Shift Left 5

• Reflection over

  y-axis

  and

  Shift Right 5

• Reflection over

  y-axis

  and

  Shift Up 5

• Reflection over

  x-axis

  and

  Shift Up 5

• Quadratic

• Linear

• Absolute Value

• Cubic

• Squaring

• Cube Root

• Cubic

• Square Root

• Cube Root

• Square Root

• Cubic

• Quadratic

• Linear

• Cubic

• Constant

• There is no name for this function

Describe the parent graph transformation

• stretch by 1/2, left 1, down 3

• stretch by 1/2, right 1, down 3

• compression by 1/2, left 1, down 3

• compression by 1/2, right 1, down 3

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)?

• g(x) = -x³

• g(x) = x³ - 1

• g(x) = (x + 1)³

• g(x) = (x - 1)³

Identify the transformations to the step function: 

• x-axis reflection; stretch of 2; right 2; down 2

• x-axis reflection; stretch of 2; left 2; down 2

• x-axis reflection; shrink of 2; left 2; up 2

• shrink of -2; right 2; down 2

Which equation is a quadratic function reflected over the x-axis and shifted up 2.

• y = x² + 2

• y = -x² + 2

• y = x² - 2

• y = -(x + 2)²