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 does the notation f(x) mean in a piecewise function?

Back

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

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.

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.

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 indicate open or closed circles at endpoints.

Tags

CCSS.HSF-IF.C.7B

Front

What is the significance of the endpoints in a piecewise function?

Back

Endpoints determine whether the function includes or excludes certain values, affecting continuity and the overall graph.

Tags

CCSS.HSF-IF.C.7B

Front

What is the value of f(0) if f(x) = 0.5x + 2.5 for x < 1 and f(x) = 2x - 1 for x ≥ 1?

Back

f(0) = 2.5.

Tags

CCSS.HSF.IF.A.2

Front

If f(x) = -x + 4 for x < 2 and f(x) = 2x - 6 for x ≥ 2, what is f(3)?

Back

f(3) = 0.

Tags

CCSS.HSF.IF.A.2

Front

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

Back

f(-2) = 0.

Tags

CCSS.HSF.IF.A.2