Absolute Value Functions

Front

What is an absolute value function?

Back

An absolute value function is a function that contains an absolute value expression. It is defined as f(x) = |x|, which outputs the non-negative value of 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 if the coefficient of the absolute value is positive and downwards if negative.

Front

What is the vertex of the function f(x) = |x - h| + k?

Back

The vertex of the function f(x) = |x - h| + k is the point (h, k), which is the minimum point of the graph.

Front

How does the value of 'k' affect the graph of f(x) = |x| + k?

Back

The value of 'k' shifts the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

What is the effect of a negative coefficient in front of the absolute value, such as in f(x) = -|x|?

Back

A negative coefficient reflects the graph of the absolute value function across the x-axis, resulting in an inverted V-shape.

Front

What is the equation of the absolute value function that has a vertex at (3, -2)?

Back

The equation is f(x) = |x - 3| - 2.

Front

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

Back

To find the x-intercepts, set the function equal to zero and solve for x.

Front

What is the domain of an absolute value function?

Back

The domain of an absolute value function is all real numbers, or (-∞, ∞).

Front

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

Back

The range of f(x) = |x| is [0, ∞), meaning it includes all non-negative real numbers.

Front

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

Back

The transformation affects the graph by scaling it vertically by a factor of 'a', shifting it horizontally by 'h', and shifting it vertically by 'k'.