Key Features of Absolute Value Functions

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that outputs the distance of a number from zero on the number line, represented as f(x) = |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.

Front

What does the vertex of an absolute value function represent?

Back

The vertex represents the highest or lowest point of the graph, depending on whether the function opens upwards or downwards.

Front

How do you find the vertex of the function f(x) = a|bx + c| + d?

Back

The vertex can be found at the point (-c/b, d) when a > 0 (opens upwards) or at (-c/b, d) when a < 0 (opens downwards).

Front

What is the significance of the 'a' value in the function f(x) = a|bx + c| + d?

Back

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

Front

What is the range of an absolute value function that opens upwards?

Back

The range is [d, ∞) where d is the y-coordinate of the vertex.

Front

What is the range of an absolute value function that opens downwards?

Back

The range is (-∞, d] where d is the y-coordinate of the vertex.

Front

How do you determine the x-intercepts of an absolute value function?

Back

Set the function equal to zero and solve for x. The solutions are the x-intercepts.

Front

What is the minimum value of an absolute value function that opens upwards?

Back

The minimum value is the y-coordinate of the vertex.

Front

What is the maximum value of an absolute value function that opens downwards?

Back

The maximum value is the y-coordinate of the vertex.