Absolute Value Functions

Front

What is the vertex of the absolute value function f(x) = |2x - 6| + 4?

Back

The vertex is (3, 4).

Front

How do you shift the graph of y = |x| to the right by 4 units?

Back

The transformation is y = |x - 4|.

Front

Write the absolute value function for a vertical stretch of 2, horizontal shift left 1 unit, and vertical shift down 9 units.

Back

f(x) = 2|x + 1| - 9.

Front

What is the transformation of the equation y = |x + 2| - 5 from the parent function y = |x|?

Back

The transformation is left 2 units and down 5 units.

Front

What is the equation of the graph represented by f(x) = -|x - 2|?

Back

The equation is f(x) = -|x - 2|.

Front

What does the absolute value function represent graphically?

Back

The absolute value function represents the distance from the x-axis.

Front

What is the general form of an absolute value function?

Back

The general form is f(x) = a|bx - h| + k, where (h, k) is the vertex.

Front

How does the value of 'a' affect the graph of an absolute value function?

Back

The value of 'a' affects the vertical stretch or compression and the direction of the graph (upward if a > 0, downward if a < 0).

Front

What is the effect of a horizontal shift in an absolute value function?

Back

A horizontal shift moves the graph left or right, depending on the sign of the value subtracted from x.

Front

What does a vertical shift do to the graph of an absolute value function?

Back

A vertical shift moves the graph up or down, depending on the value added or subtracted.