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.

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.

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.

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.

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.

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.

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.

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.