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.

Tags

CCSS.HSF-IF.C.7B

Front

How do you evaluate a piecewise function?

Back

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

Tags

CCSS.HSF.IF.A.2

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 does 'DNE' stand for in the context of functions?

Back

DNE stands for 'Does Not Exist', indicating that a function value is not defined for a particular input.

Front

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

Back

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

Tags

CCSS.HSF.IF.A.2

Front

If g(x) = { -x - 3 for x < 0; x + 10 for x ≥ 0, what is g(7)?

Back

g(7) = 7 + 10 = 17.

Tags

CCSS.HSF.IF.A.2

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What is the value of f(0) if f(x) = { x^2 - 2 for x < 0; 2x + 4 for x ≥ 0?

Back

f(0) = 2(0) + 4 = 4.

Tags

CCSS.HSF.IF.A.2

Front

What are domain restrictions in piecewise functions?

Back

Domain restrictions specify the intervals for which each piece of the function is valid.

Tags

CCSS.HSF-IF.C.7B

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 dots based on the inclusivity of the endpoints.

Tags

CCSS.HSF-IF.C.7B

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.

Tags

CCSS.HSF-IF.C.7B