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?

Back

To evaluate a piecewise function, identify the interval that contains the input value and use the corresponding expression to find the output.

Tags

CCSS.HSF.IF.A.2

Front

What does the notation f(x) mean in a piecewise function?

Back

f(x) represents the output of the function for a given input x.

Front

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

Back

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

Tags

CCSS.HSF.IF.A.2

Front

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

Back

f(1) = 3.

Tags

CCSS.HSF.IF.A.2

Front

What is the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all possible input values (x) for which the function is defined.

Front

What is the range of a piecewise function?

Back

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

Tags

CCSS.HSF-IF.C.7B

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function on its respective interval and ensure to use open or closed dots based on the inclusion of endpoints.

Tags

CCSS.HSF-IF.C.7B

Front

What is the significance of the endpoints in a piecewise function?

Back

Endpoints determine whether the function includes or excludes certain values, affecting the continuity of the graph.

Tags

CCSS.HSF-IF.C.7B

Front

How many pieces does the function f(x) = { x^2 for x < 0; 2 for 0 <= x < 2; x + 1 for x >= 2 have?

Back

This function has 3 pieces.

Tags

CCSS.HSF-IF.C.7B