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.

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.

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.

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.

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.

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.

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.

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.