Function Transformations Quiz

The graph of g(x) is the image of f(x) = x² after a reflection over the x-axis, a vertical translation of 4 units up, and a horizontal translation of 3 units to the right. Which equation represents g(x)?

• g(x) = -(x - 3)² + 4

• g(x) = -(x + 3)² - 4

• g(x) = (x - 3)² + 4

• g(x) = (x + 3)² - 4

What is the parent function for the family of functions h(x) = ½x²?

• f(x) = x

• f(x) = x²

• f(x) = |x|

• f(x) = 1

The graph of p(x) = -x² is a transformation of the parent quadratic function f(x) = x². What is the specific transformation?

• A translation 1 unit left

• A translation 1 unit down

• A reflection in the x-axis

• A reflection in the y-axis

The graph of g(x) = 2|x| is a vertical stretch of the parent absolute value function. By what factor is the graph stretched?

• ½

• 1

• 2

• -2

The graph of h(x) = |x - 3| + 1 is a transformation of f(x) = |x + 3| + 1. What is the transformation?

• A reflection in the x-axis

• A reflection in the y-axis

• A translation 6 units left

• A translation 6 units right

Which function family is described as having a V-shaped graph?

• Linear

• Absolute Value

• Quadratic

• Constant

A function g is a translation 3 units down of the graph of f(x) = 2x + 1. Which equation represents g(x)?

• g(x) = 2x + 4

• g(x) = 2x - 2

• g(x) = 2x - 3

• g(x) = 2x + 3

• A translation 4 units right and 1 unit up

• A translation 4 units left and 1 unit down

• A translation 4 units right and 1 unit down

• A translation 4 units left and 1 unit up

What is the y-intercept of the linear function g(x) = x - 4?

• (0, 4)

• (4, 0)

• (0, -4)

• (-4, 0)

• A horizontal shrink by a factor of 2 and a translation 3 units up

• A horizontal shrink by a factor of 2 and a translation 3 units down

• A horizontal stretch by a factor of 2 and a translation 3 units up

• A horizontal stretch by a factor of 2 and a translation 3 units down