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 distance of x from 0 on the number line, always resulting in a non-negative value.

Front

What does the vertex of an absolute value function represent?

Back

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

Front

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

Back

A horizontal translation shifts the graph left or right. For f(x) = |x - h|, the graph shifts right by h units if h is positive and left by h units if h is negative.

Front

What is the effect of a vertical stretch on an absolute value function?

Back

A vertical stretch increases the steepness of the graph. For example, in f(x) = a|x|, if a > 1, the graph stretches vertically.

Front

What does a vertical shrink mean in the context of absolute value functions?

Back

A vertical shrink decreases the steepness of the graph. For example, in f(x) = a|x|, if 0 < a < 1, the graph shrinks vertically.

Front

What is the transformation represented by f(x) = |x + 3| - 2?

Back

This function represents a horizontal translation left 3 units and a vertical translation down 2 units.

Front

How do you find the value of A in the function f(x) = A|x - 4| + 3?

Back

The value of A determines the vertical stretch or shrink of the graph. If A is negative, the graph opens downwards.

Front

What is the significance of the constant term in an absolute value function?

Back

The constant term affects the vertical position of the graph. It translates the graph up or down depending on its value.

Front

What does the expression |x + 4| represent in terms of transformations?

Back

The expression |x + 4| represents a horizontal translation left 4 units from the origin.

Front

How do you determine the vertex of the function f(x) = -2|x + 3| - 2?

Back

To find the vertex, identify the transformations: the vertex is at (-3, -2) after applying the horizontal translation left 3 units and vertical translation down 2 units.