Absolute Value functions

Front

What is an absolute value function?

Back

An absolute value function is a function that outputs the non-negative value of its input, defined as f(x) = |x|.

Front

What does the graph of an absolute value function look like?

Back

The graph of an absolute value function is a V-shape, opening upwards.

Front

What is the vertex of the function f(x) = |x - 3| + 2?

Back

The vertex is the point (3, 2).

Front

How does the graph of f(x) = |x| + k shift vertically?

Back

The graph shifts vertically upwards by k units if k > 0 and downwards if k < 0.

Front

What effect does a negative sign in front of an absolute value function have?

Back

It reflects the graph over the x-axis.

Front

What is the domain of any absolute value function?

Back

The domain is all real numbers, expressed as (-infinity, infinity).

Front

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

Back

The range is [0, infinity).

Front

How do you determine the x-intercepts of an absolute value function?

Back

Set the function equal to zero and solve for x.

Front

What is the effect of a horizontal shift in the function f(x) = |x - h|?

Back

The graph shifts h units to the right if h > 0 and h units to the left if h < 0.

Front

What is the equation of the absolute value function with vertex at (h, k)?

Back

The equation is f(x) = |x - h| + k.