Transformations of Absolute Value Functions

Front

What is the parent function of absolute value functions?

Back

The parent function of absolute value functions is f(x) = |x|.

Front

What does a vertical shrink by a factor of 1/9 do to the absolute value function?

Back

It compresses the graph vertically, making it wider.

Front

How do you write an absolute value function that is vertically stretched by a factor of 4/3?

Back

g(x) = (4/3)|x|.

Front

What is the effect of translating the function f(x) = |x| down 9 units?

Back

The new function is g(x) = |x| - 9.

Front

What does a vertical translation of 3 units up do to the function f(x) = |x|?

Back

The new function is g(x) = |x| + 3.

Front

Describe the transformation of the function g(x) = -2|x - 3| + 3 from the parent function f(x) = |x|.

Back

It is reflected over the x-axis, vertically stretched by a factor of 2, translated right 3 units, and translated up 3 units.

Front

What is the effect of a negative coefficient in front of an absolute value function?

Back

It reflects the graph over the x-axis.

Front

What does a vertical stretch by a factor of k do to the graph of an absolute value function?

Back

It makes the graph narrower.

Front

How do you determine the transformations applied to the parent function f(x) = |x| to obtain g(x) = (1/9)|x|?

Back

The transformation is a vertical shrink by a factor of 1/9.

Front

What is the general form of an absolute value function after transformations?

Back

g(x) = a|bx - h| + k, where a is the vertical stretch/shrink, b affects the horizontal stretch/shrink, h is the horizontal translation, and k is the vertical translation.