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 determine the value of a piecewise function at a specific point?

Back

To determine the value of a piecewise function at a specific point, identify which interval the point falls into and use the corresponding expression.

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, which may depend on the interval in which x lies.

Front

What is the significance of the domain in piecewise functions?

Back

The domain of a piecewise function specifies 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, ensuring to use open or closed dots as appropriate.

Tags

CCSS.HSF-IF.C.7B

Front

What is the difference between an open interval and a closed interval?

Back

An open interval does not include its endpoints, while a closed interval includes its endpoints.

Tags

CCSS.6.EE.B.8

Front

If f(x) = -x + 4 for x < 2, what is f(1)?

Back

f(1) = -1 + 4 = 3.

Front

If f(x) = 2x - 6 for x >= 2, what is f(3)?

Back

f(3) = 2(3) - 6 = 0.

Tags

CCSS.HSF.IF.A.2

Front

How many pieces are in the function f(x) = { -x + 4 if x < 2; 2x - 6 if x >= 2 }?

Back

There are 2 pieces in this function.

Tags

CCSS.HSF-IF.C.7B

Front

What is the value of f(2) in the function f(x) = { -x + 4 if x < 2; 2x - 6 if x >= 2 }?

Back

f(2) = 2(2) - 6 = -2.

Tags

CCSS.HSF.IF.A.2