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 at a specific point?

Back

To evaluate a piecewise function at a specific point, determine which interval the point falls into and use the corresponding expression to find the function's value.

Tags

CCSS.HSF.IF.A.2

Front

What does 'DNE' stand for in the context of functions?

Back

DNE stands for 'Does Not Exist', indicating that the function does not have a value at that particular input.

Tags

CCSS.HSF.IF.A.2

Front

If f(x) = { x + 2 for x < 0; x^2 for x >= 0, what is f(-1)?

Back

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

Tags

CCSS.HSF.IF.A.2

Front

If f(x) = { 3x for x < 1; 2x + 1 for x >= 1, what is f(2)?

Back

f(2) = 2(2) + 1 = 5.

Tags

CCSS.HSF.IF.A.2

Front

What is the value of f(0) if f(x) = { 2x for x < 0; 4 for x = 0; x + 1 for x > 0?

Back

f(0) = 4.

Tags

CCSS.HSF.IF.A.2

Front

How do you graph a piecewise function?

Back

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

Tags

CCSS.HSF-IF.C.7B

Front

What is the significance of the domain in piecewise functions?

Back

The domain of a piecewise function specifies the intervals over which each piece of the function is valid.

Tags

CCSS.HSF-IF.C.7B

Front

If f(x) = { x^2 for x < 1; 3 for x = 1; 2x for x > 1, what is f(1)?

Back

f(1) = 3.

Tags

CCSS.HSF.IF.A.2

Front

What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all possible output values (y-values) that the function can produce.

Tags

CCSS.HSF-IF.C.7B