Piecewise functions 2

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.

Tags

CCSS.HSF.IF.A.2

Front

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

Back

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

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

Front

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

Back

f(-2) = 3(-2) + 2 = -6 + 2 = -4.

Tags

CCSS.HSF.IF.A.2

Front

What is the value of f(4) if f(x) = 3x + 2 for x < 0 and f(x) = x^2 for x >= 0?

Back

f(4) = 4^2 = 16.

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 circles to indicate whether endpoints are included.

Tags

CCSS.HSF-IF.C.7B

Front

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

Back

Breakpoints are the values at which the function changes from one expression to another, and they are crucial for determining the intervals of the function.

Tags

CCSS.HSF-IF.C.7B

Front

If a delivery service charges $11 for packages weighing 2 pounds or less and $3 for each additional pound, what is the function for weights greater than 2 pounds?

Back

The function is f(x) = 11 + 3(x - 2) for x > 2.