Absolute Value Graph Transformations

Front

What is the definition of absolute value?

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

How does the graph of y = |x| look?

Back

The graph of y = |x| is a V-shaped graph that opens upwards, with its vertex at the origin (0,0).

Front

What effect does adding a constant outside the absolute value have on the graph?

Back

Adding a constant outside the absolute value function shifts the graph vertically. For example, y = |x| + 2 shifts the graph up by 2 units.

Front

What effect does subtracting a constant outside the absolute value have on the graph?

Back

Subtracting a constant outside the absolute value function shifts the graph vertically down. For example, y = |x| - 3 shifts the graph down by 3 units.

Front

What effect does adding a constant inside the absolute value have on the graph?

Back

Adding a constant inside the absolute value function shifts the graph horizontally. For example, y = |x + 4| shifts the graph left by 4 units.

Front

What effect does subtracting a constant inside the absolute value have on the graph?

Back

Subtracting a constant inside the absolute value function shifts the graph horizontally to the right. For example, y = |x - 5| shifts the graph right by 5 units.

Front

What does a negative coefficient in front of the absolute value indicate?

Back

A negative coefficient in front of the absolute value function reflects the graph across the x-axis. For example, y = -|x| opens downwards.

Front

How do you determine the vertex of the graph y = |x - h| + k?

Back

The vertex of the graph y = |x - h| + k is at the point (h, k). This is the point where the graph changes direction.

Front

What is the transformation of the graph y = |x| when the equation is y = |x - 3| + 2?

Back

The graph is shifted right by 3 units and up by 2 units.

Front

How do you find the x-intercepts of the graph y = |x - 1|?

Back

To find the x-intercepts, set y = 0: 0 = |x - 1|, which gives x = 1.