Absolute value functions and graphs

Front

What is the absolute value of a number?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative.

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is f(x) = |x|, which creates a V-shaped graph.

Front

How does the graph of f(x) = |x| change when a constant is added?

Back

Adding a constant shifts the graph vertically. For example, f(x) = |x| + 3 shifts the graph up by 3 units.

Front

What effect does multiplying the absolute value function by a negative number have?

Back

Multiplying by a negative number reflects the graph across the x-axis.

Front

What does the expression |x + 2| represent?

Back

It represents a horizontal shift of the absolute value function to the left by 2 units.

Front

How do you determine the vertex of the function f(x) = a|x - h| + k?

Back

The vertex is at the point (h, k), where h is the horizontal shift and k is the vertical shift.

Front

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

Back

A vertical shrink by a factor of a (0 < a < 1) makes the graph wider.

Front

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

Back

A vertical stretch by a factor of a (a > 1) makes the graph narrower.

Front

Describe the transformation of f(x) = |x| - 4.

Back

This function shifts the graph of the absolute value function down by 4 units.

Front

What is the interval where the function f(x) = |x - 3| is decreasing?

Back

The function is decreasing on the interval (-inf, 3).