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 then use the corresponding expression to find the function's value.

Tags

CCSS.HSF.IF.A.2

Front

What does the notation f(x) = { expression1 if condition1; expression2 if condition2; ... } represent?

Back

This notation represents a piecewise function where each expression is used based on the condition that is satisfied by the input x.

Front

How can you determine the number of pieces in a piecewise function?

Back

The number of pieces in a piecewise function is determined by the number of different expressions or formulas defined for different intervals of the domain.

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 input values for which each piece of the function is valid.

Tags

CCSS.HSF-IF.C.7B

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, ensuring to use open or closed circles to indicate whether endpoints are included.

Tags

CCSS.HSF-IF.C.7B

Front

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

Back

f(-2) = 2(-2) + 4 = 0.

Tags

CCSS.HSF.IF.A.2

Front

How do you match a graph to its corresponding piecewise function?

Back

To match a graph to its corresponding piecewise function, analyze the behavior of the graph in different intervals and identify the equations that describe those behaviors.

Tags

CCSS.HSF-IF.C.7B

Front

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

Back

f(0) = 1.

Tags

CCSS.HSF.IF.A.2

Front

What is the formula for a piecewise function that is defined as f(x) = { -x + 1 if x < 4; x if x >= 4 }?

Back

The formula is f(x) = { -x + 1 for x < 4; x for x >= 4 }.