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.

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-values) for which the function is defined.

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

Evaluate f(-1) if f(x) = { 2x + 4 for x < 0; -x + 1 for x >= 0 }

Back

f(-1) = 2(-1) + 4 = 2.

Front

Evaluate f(-2) if f(x) = { x^2 for x < 0; 3 for x >= 0 }

Back

f(-2) = (-2)^2 = 4.

Front

Evaluate f(2) if f(x) = { x - 3 for x < 0; 2x + 1 for x >= 0 }

Back

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

Front

What does DNE stand for in the context of functions?

Back

DNE stands for 'Does Not Exist', indicating that a function value is undefined at a certain point.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function on its respective interval and ensure to use open or closed circles to indicate whether endpoints are included.

Front

What is a common mistake when evaluating piecewise functions?

Back

A common mistake is using the wrong expression for a given input value, often due to not correctly identifying the interval.