Absolute Value Transformations

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 does the transformation y = |x| + k represent?

Back

This transformation shifts the graph of y = |x| vertically by k units. If k is positive, it shifts up; if k is negative, it shifts down.

Front

What does the transformation y = -|x| represent?

Back

This transformation reflects the graph of y = |x| across the x-axis.

Front

How does the coefficient in front of the absolute value affect the graph?

Back

A coefficient greater than 1 vertically stretches the graph, while a coefficient between 0 and 1 vertically compresses it.

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is y = |x|.

Front

What does a horizontal shift of h units to the right look like in an absolute value function?

Back

The transformation is represented as y = |x - h|.

Front

What does a vertical shift of k units up look like in an absolute value function?

Back

The transformation is represented as y = |x| + k.

Front

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

Back

It reflects the graph across the x-axis.

Front

How do you write an absolute value function that is vertically stretched by a factor of a?

Back

The function is written as y = a|x|.

Front

What does the transformation y = |x + 3| represent?

Back

This transformation shifts the graph of y = |x| left by 3 units.