Absolute Value Functions

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that contains an algebraic expression within absolute value symbols, which measures the distance of a number from zero on the number line, always resulting in a non-negative output.

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 'a' in the absolute value function affect?

Back

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

Front

What does the 'b' in the absolute value function affect?

Back

The 'b' value affects the horizontal stretch or compression of the graph.

Front

What does the 'c' in the absolute value function represent?

Back

The 'c' value represents a horizontal shift of the graph to the left or right.

Front

What does the 'd' in the absolute value function represent?

Back

The 'd' value represents a vertical shift of the graph up or down.

Front

What is the vertex of an absolute value function?

Back

The vertex is the point where the graph changes direction, typically represented as (h, k) in the function f(x) = a|bx + c| + d.

Front

How do you find the vertex of the function f(x) = -|2x + 6| + 5?

Back

To find the vertex, set the expression inside the absolute value to zero: 2x + 6 = 0, which gives x = -3. Then, substitute x = -3 into the function to find y: f(-3) = -|2(-3) + 6| + 5 = 1. So, the vertex is (-3, 1).

Front

What is the shape of the graph of an absolute value function?

Back

The graph of an absolute value function has a 'V' shape.

Front

What is the range of the function f(x) = -|2x + 6| + 5?

Back

The range is y < 5, since the maximum value occurs at the vertex.