Key Features and Transformations of Parent Functions

What are the transformations to the graph compared to the parent function?

• Shifted right 2, shifted up 3, and reflected over the y-axis

• Shifted left 2, shifted up 3, and reflected over the y-axis

• Shifted left 2, shifted up 3, and reflected over the x-axis

• Shifted right 2, shifted up 3, and reflected over the x-axis

Describe the transformations from the original parent function f(x) = x².
g(x) = 5x² + 2

• Vertical Stretch of 5
  Down 2

• Vertical Shrink of 5
  Up 2

• Vertical Stretch of 5
  Up 2

• Vertical Shrink of 5
  Down 2

Which equation transforms f(x) = x to a horizontal stretch by a factor of 2, a reflection over the x axis, and a shift down 4?

• f(-2x - 4)

• f(-1/2x) - 4

• -f(2x) - 4

• -f(1/2x) - 4

If the blue is f(x)=x^2, the red must be

• g(x)=(x+3)²

• g(x)=(x-3)²

• g(x)=x²+3

• g(x)=x²-2

Write an absolute value function given the following transformations:
Reflection across the x-axis
Vertical shift right 2 units
Horizontal shift down 7 units

• y = -|x + 2| - 7 

• y = |x - 2| - 7 

• y = -|x - 2| - 7

• y = -|x - 2| + 7

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

Write the equation that results if the parent absolute value function is shifted right 15 units, down 3 units, and reflected vertically.

Describe the transformation(s) in the following function.