Major Assessment #1: Functions Overview

Given the function f(x) = x², which transformation would result in the graph of f(x) being shifted 3 units to the right?

• f(x) = (x - 3)^2

• f(x) = (x + 3)^2

• f(x) = x^2 + 3

• f(x) = x^2 - 3

Match the parent function with its graph's description

• y = |x|

• A straight line passing through the origin

• y = x

• A graph that starts at the origin and increases slowly

• A v-shaped graph centered at the origin

• y = x²

• A parabola opening upwards centered at the origin

Match the parent function with its range

• Nonlinear with two ends pointing in opposite directions

• Nonlinear with an endpoint at the origin

• Nonlinear with a minimum point

• Nonlinear with a sharp turn at the origin

What is the effect of the transformation f(x) = -2 * g(x) on the graph of the function g(x)?

• Vertical stretch by a factor of 2 and reflection in the x-axis

• Vertical compression by a factor of 2 and reflection in the x-axis

• Vertical stretch by a factor of 2 and reflection in the y-axis

• Vertical compression by a factor of 2 and reflection in the y-axis

If h(x) = 1/4 * f(x), how is the graph of h(x) related to the graph of f(x)?

• It is horizontally stretched by a factor of 4

• It is horizontally compressed by a factor of 4

• It is vertically stretched by a factor of 4

• It is vertically compressed by a factor of 4

The function f(x) = (x - 2)² + 5 is a transformation of the parent function g(x) = x².

Describe the transformation.

• Shifted 2 units to the right and 5 units up

• Shifted 2 units to the left and 5 units up

• Shifted 2 units to the right and 5 units down

• Shifted 2 units to the left and 5 units down

What is the effect of the transformation f(x) = g(x + 4) - 1 on the graph of the function g(x)?

• Shifted 4 units to the left and 1 unit up

• Shifted 4 units to the right and 1 unit up

• Shifted 4 units to the left and 1 unit down

• Shifted 4 units to the right and 1 unit down

If the graph of f(x) = |x| is reflected over the x-axis, what is the new equation?

• f(x) = -|x|

• f(x) = |x|

• f(x) = |x| + 1

• f(x) = -|x| - 1

Given the function f(x) = x³, which transformation would result in the graph of f(x) being reflected over the y-axis?

• f(x) = -x^3

• f(x) = (x + 3)^3

• f(x) = (-x)^3

• f(x) = x^3 + 3

What is the result of the transformation f(x) = 3 * g(x - 2) on the graph of the function g(x)?

• Stretched vertically by a factor of 3 and shifted 2 units to the right

• Stretched vertically by a factor of 3 and shifted 2 units to the left

• Compressed vertically by a factor of 3 and shifted 2 units to the right

• Compressed vertically by a factor of 3 and shifted 2 units to the left