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 at a specific point?

Back

To evaluate a piecewise function at a specific point, determine which interval the point falls into and use the corresponding expression to find the function's value.

Front

What does DNE stand for in the context of functions?

Back

DNE stands for 'Does Not Exist', indicating that a function does not have a value at a certain point.

Front

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

Back

f(-2) = 4, since -2 falls in the interval x < 0.

Front

If g(x) = { -x - 5 for x < -1; x + 3 for x >= -1, what is g(-2)?

Back

g(-2) = 7, since -2 falls in the interval x < -1.

Front

Evaluate f(-3) if f(x) = { -x - 4 for x < -2; 2x + 1 for x >= -2.

Back

f(-3) = -7, since -3 falls in the interval x < -2.

Front

What is the value of f(0) if f(x) = { 3x + 1 for x < 1; x^2 for x >= 1?

Back

f(0) = 4, since 0 falls in the interval x < 1.

Front

Back

f(-8) = 21, since -8 falls in the interval x < -5.

Front

What is the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all possible input values (x) for which the function is defined, often expressed in intervals.

Front

What is the range of a piecewise function?

Back

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