Graphing 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) = { x if x < 4; -x+1 if x ≥ 4 mean?

Back

This notation means that for values of x less than 4, f(x) equals x, and for values of x greater than or equal to 4, f(x) equals -x + 1.

Front

How many pieces are in the function f(x) = { -x+1 if x < 4; x if x ≥ 4?

Back

There are 2 pieces in this function.

Tags

CCSS.HSF-IF.C.7B

Front

What is the value of f(-2) for the function f(x) = { -x+1 if x < 4; x if x ≥ 4?

Back

f(-2) = -(-2) + 1 = 3.

Tags

CCSS.HSF.IF.A.2

Front

What is the value of f(2) for the function f(x) = { -x+1 if x < 4; x if x ≥ 4?

Back

f(2) = 2 because 2 is greater than or equal to 4.

Tags

CCSS.HSF.IF.A.2

Front

What is the significance of the point where the pieces of a piecewise function meet?

Back

The point where the pieces meet is called a 'breakpoint' and is important for determining the continuity of the function.

Tags

CCSS.HSF-IF.C.7B

Front

How can you graph a piecewise function?

Back

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

Tags

CCSS.HSF-IF.C.7B

Front

What is the domain of the function f(x) = { -x+1 if x < 4; x if x ≥ 4?

Back

The domain of this function is all real numbers, as it is defined for every x.

Front

What is the range of the function f(x) = { -x+1 if x < 4; x if x ≥ 4?

Back

The range is all real numbers greater than or equal to -3.