1.6 Absolute Value Transformations

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is f(x) = |x|.

Front

What transformation does g(x) = |x - 2| represent?

Back

A horizontal shift of the graph of f(x) = |x| to the right by 2 units.

Front

What transformation does g(x) = |x + 2| represent?

Back

A horizontal shift of the graph of f(x) = |x| to the left by 2 units.

Front

What transformation does g(x) = |x| + 2 represent?

Back

A vertical shift of the graph of f(x) = |x| upward by 2 units.

Front

What transformation does g(x) = |x| - 2 represent?

Back

A vertical shift of the graph of f(x) = |x| downward by 2 units.

Front

What transformation does g(x) = -|x| represent?

Back

A reflection of the graph of f(x) = |x| over the x-axis.

Front

What transformation does g(x) = -|x| + 2 represent?

Back

A reflection of the graph of f(x) = |x| over the x-axis and a vertical shift upward by 2 units.

Front

What does a vertical stretch of the absolute value function look like?

Back

A vertical stretch is represented by g(x) = a|x| where a > 1.

Front

What does a vertical compression of the absolute value function look like?

Back

A vertical compression is represented by g(x) = a|x| where 0 < a < 1.

Front

What is the effect of a horizontal shift on the graph of f(x) = |x|?

Back

A horizontal shift moves the graph left or right without changing its shape.