3.7 Graphing Absolute Value Functions

Front

What is an absolute value function?

Back

An absolute value function is a function that contains an absolute value expression, typically in the form f(x) = |x|, which measures the distance of x from zero on the number line.

Front

What is the vertex of the absolute value function f(x) = |x - h| + k?

Back

The vertex of the function is the point (h, k), which represents the minimum or maximum point of the graph.

Front

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

Back

A vertical stretch multiplies the output of the function by a factor greater than 1, making the 'V' shape of the graph narrower.

Front

What does a horizontal shift to the left by 3 units look like in the function f(x) = |x + 3|?

Back

The graph of the function shifts left by 3 units, moving the vertex from (0,0) to (-3,0).

Front

What is the effect of a vertical shift up by 4 units on the function f(x) = |x|?

Back

The graph shifts up by 4 units, moving the vertex from (0,0) to (0,4), resulting in f(x) = |x| + 4.

Front

What does it mean to reflect a graph over the x-axis?

Back

Reflecting a graph over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

How do you write the absolute value function for a vertical stretch of 2 and a vertical shift down 3?

Back

The function can be written as f(x) = 2|x| - 3.

Front

What is the transformation of the function f(x) = -|x|?

Back

The function is reflected over the x-axis, resulting in a 'V' shape that opens downward.

Front

What does the expression |x - 5| represent on a graph?

Back

It represents a V-shaped graph with the vertex at (5,0) and opens upwards.

Front

How do you determine the vertex of the function y = -4|x + 2| + 5?

Back

The vertex is found at the point (-2, 5), where the function reaches its maximum value.