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

What does the transformation f(x) = |x| + k represent?

Back

This transformation shifts the graph of the absolute value function vertically by k units. If k is positive, it shifts up; if k is negative, it shifts down.

Front

What does the transformation f(x) = |x - h| represent?

Back

This transformation shifts the graph of the absolute value function horizontally by h units. If h is positive, it shifts right; if h is negative, it shifts left.

Front

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

Back

This transformation reflects the graph of the absolute value function across the x-axis.

Front

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

Back

A vertical stretch occurs when the function is multiplied by a factor greater than 1, making the graph steeper.

Front

What is the effect of a vertical compression on the absolute value function?

Back

A vertical compression occurs when the function is multiplied by a factor between 0 and 1, making the graph flatter.

Front

How does the transformation f(x) = -|x| + k affect the graph?

Back

This transformation reflects the graph across the x-axis and then shifts it vertically by k units.

Front

What does the transformation f(x) = |x| - k represent?

Back

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

Front

What is the transformation of the graph y = |x| + 3?

Back

The graph shifts up 3 units.

Front

What is the transformation of the graph y = |x - 2|?

Back

The graph shifts right 2 units.