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. It is defined as f(x) = |x|, which outputs the non-negative value of x.

Front

What does the graph of y = |x| look like?

Back

The graph of y = |x| is a V-shaped graph that opens upwards, with the vertex at the origin (0,0).

Front

How does the equation y = |x + 2| differ from y = |x|?

Back

The equation y = |x + 2| shifts the graph of y = |x| to the left by 2 units.

Front

What effect does the equation y = |x - 3| have on the graph of y = |x|?

Back

The equation y = |x - 3| shifts the graph of y = |x| to the right by 3 units.

Front

What is the vertex of the graph of y = |x - 5|?

Back

The vertex of the graph of y = |x - 5| is at the point (5, 0).

Front

How does the coefficient in front of the absolute value affect the graph?

Back

A coefficient greater than 1 stretches the graph vertically, while a coefficient between 0 and 1 compresses it vertically.

Front

What does the equation y = |x| + 2 represent?

Back

The equation y = |x| + 2 shifts the graph of y = |x| upwards by 2 units.

Front

What does the equation y = |x| - 2 represent?

Back

The equation y = |x| - 2 shifts the graph of y = |x| downwards by 2 units.

Front

What is the general form of an absolute value function?

Back

The general form of an absolute value function is f(x) = a|bx + c| + d, where a, b, c, and d are constants.

Front

How do you determine the x-intercepts of the graph of y = |x - 2|?

Back

To find the x-intercepts, set y = 0: 0 = |x - 2|, which gives x = 2.