ALG1H 4.7 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 the input variable.

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.

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

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

Back

f(4) = 4, since x = 4 falls into the second part of the piecewise function.

Front

How do you graph a piecewise function?

Back

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

Front

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

Back

f(2) = 1, since 2 is less than 4, we use the first expression: -2 + 1 = -1.

Front

What is the output of f(0) for the function f(x) = { -x + 1 if x < 4; x if x ≥ 4?

Back

f(0) = 1, since 0 is less than 4, we use the first expression: -0 + 1 = 1.

Front

What is the significance of the point where the piecewise function changes?

Back

The point where the piecewise function changes is called a breakpoint, and it is where the function's rule changes, affecting the output.

Front

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

Back

The domain is all real numbers, as there are no restrictions on the input values.

Front

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

Back

The range is all real numbers, as the function can take any value depending on the input.