Graphing Absolute Value Functions

Front

What is 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' affects the vertical stretch or compression, 'b' affects the horizontal stretch or compression, 'c' shifts the graph horizontally, and 'd' shifts it vertically.

Front

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

Back

The value of 'a' determines the vertical stretch or compression of the graph. If 'a' is positive, the graph opens upwards; if 'a' is negative, it opens downwards.

Front

What effect does changing 'b' have on the graph of an absolute value function?

Back

The value of 'b' affects the horizontal stretch or compression. If |b| > 1, the graph is compressed horizontally; if |b| < 1, it is stretched horizontally.

Front

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

Back

The 'c' value shifts the graph horizontally. If 'c' is positive, the graph shifts to the left; if 'c' is negative, it shifts to the right.

Front

What is the role of 'd' in the absolute value function?

Back

The 'd' value shifts the graph vertically. If 'd' is positive, the graph shifts up; if 'd' is negative, it shifts down.

Front

How do you identify the vertex of an absolute value function?

Back

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

Front

What is the effect of a negative sign in front of an absolute value function?

Back

A negative sign in front of the absolute value function reflects the graph across the x-axis.

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, with points at (1, 1) and (3, 1).

Front

What is the equation of the graph of f(x) = -|x + 2| + 4?

Back

The equation represents a downward-opening V-shape with vertex at (-2, 4).