Piecewise & Absolute Value Functions

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different intervals of its domain.

Front

How do you evaluate a piecewise function?

Back

To evaluate a piecewise function, identify the interval in which the input value falls and use the corresponding expression to find the output.

Front

What is the absolute value of a number?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative.

Front

How do you graph an absolute value function?

Back

An absolute value function has a V-shape graph. The vertex is at the point where the expression inside the absolute value equals zero.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Given f(x) = |x|, what is f(-3)?

Back

f(-3) = 3.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

How do you find the maximum value of a piecewise function?

Back

To find the maximum value, evaluate the function at the endpoints of the intervals and at any critical points within the intervals.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph.

Front

How do you solve an absolute value equation?

Back

To solve an absolute value equation, set up two separate equations: one for the positive case and one for the negative case.