Evaluating 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 a function value is undefined at a certain point.

Tags

CCSS.HSF.IF.A.2

Front

If f(x) = { x^2 for x < 0; 2x + 1 for x >= 0, what is f(3)?

Back

f(3) = 2(3) + 1 = 7.

Tags

CCSS.HSF.IF.A.2

Front

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

Back

f(-2) = -2 + 2 = 0.

Tags

CCSS.HSF.IF.A.2

Front

How do you find the limit of a piecewise function as x approaches a certain value?

Back

To find the limit, evaluate the function from both sides of the point and check if both sides approach the same value.

Front

What is the significance of the domain in piecewise functions?

Back

The domain specifies the intervals over which each piece of the function is valid and helps determine which expression to use for evaluation.

Tags

CCSS.HSF-IF.C.7B

Front

If g(x) = { -x for x < 0; x^2 for x >= 0, what is g(7)?

Back

g(7) = 7^2 = 49.

Tags

CCSS.HSF.IF.A.2

Front

What is the output of f(0) if f(x) = { -3 for x < 0; 4 for x = 0; 2x 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 and ensure to use open or closed circles to indicate whether endpoints are included.

Tags

CCSS.HSF-IF.C.7B