Absolute Value 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 subtracting a constant from |x| have on its graph?

Back

Subtracting a constant from |x| shifts the graph downward. For example, y = |x| - 4 shifts the graph down by 4 units.

Front

What effect does adding a constant to |x| have on its graph?

Back

Adding a constant to |x| shifts the graph upward. For example, y = |x| + 3 shifts the graph up by 3 units.

Front

What does a vertical stretch by a factor of 2 do to the graph of y = |x|?

Back

A vertical stretch by a factor of 2 transforms the graph to y = 2|x|, making it steeper.

Front

What is the effect of a negative sign in front of |x|?

Back

A negative sign in front of |x| reflects the graph across the x-axis. For example, y = -|x| flips the V-shape downwards.

Front

How do you identify a reflection in the graph of an absolute value function?

Back

A reflection occurs when the equation has a negative sign in front of the absolute value, such as y = -|x|.

Front

What is the transformation represented by y = |x - 3|?

Back

The transformation y = |x - 3| shifts the graph of y = |x| to the right by 3 units.

Front

What is the transformation represented by y = |x + 3|?

Back

The transformation y = |x + 3| shifts the graph of y = |x| to the left by 3 units.

Front

What does the equation y = |x| - 3 represent?

Back

The equation y = |x| - 3 represents a downward shift of the graph of y = |x| by 3 units.