2A.2A Absolute Value Graphs and Transformations

Front

What is the parent function of absolute value?

Back

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

Front

What does the graph of f(x) = |x| look like?

Back

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

Front

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

Back

The graph of g(x) = |x - 2| is the graph of f(x) = |x| shifted 2 units to the right.

Front

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

Back

The graph of g(x) = |x| + 2 is the graph of f(x) = |x| shifted 2 units up.

Front

What does the negative sign in front of the absolute value function indicate?

Back

The negative sign indicates that the graph opens downwards.

Front

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

Back

A vertical stretch makes the graph narrower. For example, g(x) = 3|x| is a vertical stretch of f(x) = |x|.

Front

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

Back

A vertical compression makes the graph wider. For example, g(x) = (1/2)|x| is a vertical compression of f(x) = |x|.

Front

What is the domain of the function f(x) = |x|?

Back

The domain of f(x) = |x| is all real numbers, expressed as (-∞, +∞).

Front

What is the range of the function f(x) = |x|?

Back

The range of f(x) = |x| is all non-negative real numbers, expressed as [0, +∞).

Front

What is the domain of the function g(x) = -3|x|?

Back

The domain of g(x) = -3|x| is all real numbers, expressed as (-∞, +∞).