Evaluating Piecewise Functions

Front

What is a piecewise function?

Back

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

Front

How do you evaluate a piecewise function?

Back

To evaluate a piecewise function, identify which piece of the function applies to the given input value and then use that expression to calculate the output.

Front

What does the notation f(x) mean?

Back

f(x) represents the output of the function f for a given input x.

Front

If f(x) = { x + 2 for x < 0; x^2 for x ≥ 0, what is f(-1)?

Back

f(-1) = -1 + 2 = 1.

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

What does the notation 0 ≤ x < 2 indicate?

Back

This notation indicates that x can take any value from 0 to just below 2, including 0 but not including 2.

Front

Evaluate f(6) if f(x) = { 2x - 5 for x < 5; 3x - 1 for x ≥ 5.

Back

f(6) = 3(6) - 1 = 17.

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

If f(x) = { x^2 for x < 1; 3x for x ≥ 1, what is f(0)?

Back

f(0) = 0^2 = 0.

Front

How do you find the output of a piecewise function at a boundary point?

Back

At a boundary point, evaluate both pieces of the function to see which one applies based on the inequality.