Absolute Value 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 denoted as |x|.

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 we add a constant to it?

Back

Adding a constant shifts the graph vertically. For example, f(x) = |x| + 2 shifts the graph up by 2 units.

Front

What effect does subtracting a constant from the absolute value function have on its graph?

Back

Subtracting a constant shifts the graph down. For example, f(x) = |x| - 3 shifts the graph down by 3 units.

Front

What does the equation f(x) = |x - 2| represent?

Back

This equation represents a graph that is shifted 2 units to the right from the parent function f(x) = |x|.

Front

What does the equation f(x) = |x + 3| represent?

Back

This equation represents a graph that is shifted 3 units to the left from the parent function f(x) = |x|.

Front

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

Back

The vertex of the graph of an absolute value function f(x) = |x - h| + k is the point (h, k).

Front

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

Back

A negative sign reflects the graph across the x-axis. For example, f(x) = -|x| opens downwards.

Front

What does the equation y = |x - 3| - 2 indicate about the graph?

Back

This indicates that the graph is shifted 3 units to the right and 2 units down from the parent function.

Front

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

Back

To find the x-intercepts, set the function equal to zero and solve for x.