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.

Front

How do you determine the value of a piecewise function at a specific point?

Back

To determine the value of a piecewise function at a specific point, identify which interval the point falls into and use the corresponding expression.

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, which may depend on the interval in which x lies.

Front

What is the significance of the domain in piecewise functions?

Back

The domain of a piecewise function specifies the intervals for which each piece of the function is valid.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function on its respective interval, ensuring to use open or closed dots as appropriate.

Front

What is the difference between an open interval and a closed interval?

Back

An open interval does not include its endpoints, while a closed interval includes its endpoints.

Front

If f(x) = -x + 4 for x < 2, what is f(1)?

Back

f(1) = -1 + 4 = 3.

Front

If f(x) = 2x - 6 for x >= 2, what is f(3)?

Back

f(3) = 2(3) - 6 = 0.

Front

How many pieces are in the function f(x) = { -x + 4 if x < 2; 2x - 6 if x >= 2 }?

Back

There are 2 pieces in this function.

Front

What is the value of f(2) in the function f(x) = { -x + 4 if x < 2; 2x - 6 if x >= 2 }?

Back

f(2) = 2(2) - 6 = -2.