Exploring Transformations of Linear and Absolute Value Functions

The video tutorial covers transformations of linear and absolute value functions, including translations, reflections, stretches, and shrinks. It explains how to perform horizontal and vertical translations, reflections over the x-axis and y-axis, and how to apply stretches and shrinks. The tutorial includes practice problems to reinforce the concepts.

What is the result of translating the function f(x) = 2x + 1 three units down?

• f(x) = 2x + 4

• f(x) = 2x - 2

• f(x) = 2x - 3

• f(x) = 2x + 1

How do you translate the function f(x) = 2x + 1 two units to the left?

• f(x) = 2x + 3

• f(x) = 2(x + 2) + 1

• f(x) = 2x - 1

• f(x) = 2(x - 2) + 1

What happens to the function f(x) = |x + 3| - 1 when it is reflected over the x-axis?

• f(x) = -|x + 3| - 1

• f(x) = |x - 3| + 1

• f(x) = -|x + 3| + 1

• f(x) = |x + 3| + 1

How do you reflect the function f(x) = |x + 3| - 1 over the y-axis?

• f(x) = |-x + 3| - 1

• f(x) = |x + 3| + 1

• f(x) = |x + 3| - 1

• f(x) = |x - 3| - 1

What is the result of a horizontal shrink by a factor of 1/3 on the function f(x) = |x - 3| - 5?

• f(x) = |3x - 9| - 5

• f(x) = |x - 3| - 5

• f(x) = |x/3 - 3| - 5

• f(x) = |3x - 3| - 5

How do you perform a vertical stretch by a factor of 2 on the function f(x) = |x - 3| - 5?

• f(x) = 2|x - 3| - 10

• f(x) = |2x - 3| - 5

• f(x) = 2|x - 3| - 5

• f(x) = |x - 3| - 10

What is the effect of a horizontal stretch by a factor of 2 on the function f(x) = 4x + 2?

• f(x) = 2x + 2

• f(x) = 2x + 4

• f(x) = 4x + 4

• f(x) = 8x + 2

How do you perform a vertical shrink by a factor of 1/3 on the function f(x) = |x| - 3?

• f(x) = |x| - 3

• f(x) = 1/3|x| - 3

• f(x) = 1/3|x| - 1

• f(x) = |x| - 1

What is the general rule for a vertical transformation?

• It affects only the x-term.

• It affects the entire function.

• It does not affect the function.

• It affects only the y-term.

What is the general rule for a horizontal transformation?

• It affects only the x-term.

• It affects the entire function.

• It affects only the y-term.

• It does not affect the function.