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 is the general form of an absolute value function?

Back

The general form is f(x) = a|bx + c| + d, where a, b, c, and d are constants that affect the graph's shape and position.

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. If 'a' is positive, the graph opens upwards; if negative, it opens downwards.

Front

What does the 'c' value represent in the function f(x) = a|bx + c| + d?

Back

The 'c' value represents a horizontal shift. If 'c' is positive, the graph shifts to the left; if negative, it shifts to the right.

Front

What does the 'd' value represent in the function f(x) = a|bx + c| + d?

Back

The 'd' value represents a vertical shift. If 'd' is positive, the graph shifts upwards; if negative, it shifts downwards.

Front

What is the vertex of an absolute value function?

Back

The vertex is the point where the graph changes direction, typically found at the point (-c/b, d) in the function f(x) = a|bx + c| + d.

Front

What is the domain of an absolute value function?

Back

The domain of an absolute value function is all real numbers, expressed as (-∞, +∞).

Front

What is the range of an absolute value function?

Back

The range of an absolute value function is [d, +∞) if 'a' is positive, or (-∞, d] if 'a' is negative.

Front

How do you graph the function f(x) = |x - 2|?

Back

To graph f(x) = |x - 2|, plot the vertex at (2, 0) and create a V-shape opening upwards.

Front

How do you graph the function f(x) = -|x + 3| + 1?

Back

To graph f(x) = -|x + 3| + 1, plot the vertex at (-3, 1) and create a V-shape opening downwards.