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 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 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 'DNE' stand for in function evaluation?

Back

DNE stands for 'Does Not Exist', indicating that the function does not have a value for that input.

Front

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

Back

f(-2) = -2 + 2 = 0.

Front

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

Back

f(2) = 2(2) + 1 = 5.

Front

What is the range of a piecewise function?

Back

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

Front

How do you find the value of g(7) in a piecewise function?

Back

Identify the piece of the function that includes x = 7 and substitute 7 into that expression.

Front

What is an interval notation?

Back

Interval notation is a way of writing subsets of the real number line, using parentheses and brackets to indicate whether endpoints are included.

Front

What does the notation '-2 < x ≤ 1' mean?

Back

It means that x is greater than -2 and less than or equal to 1.