Piecewise Practice

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 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.

Front

What is the significance of the domain in piecewise functions?

Back

The domain of a piecewise function specifies the intervals over which each piece of the function is defined, which is crucial for determining the function's behavior.

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.

Front

What does f(2) = 1 indicate in a piecewise function?

Back

It indicates that when the input x is 2, the output of the function f is 1, which is a specific evaluation of the function.

Front

What is the formula for the piecewise function given in Question 2?

Back

f(x) = { -x + 1 if x < 4; x if x ≥ 4 }.

Front

How do you find the value of f(-7) in a piecewise function?

Back

To find f(-7), identify the interval that -7 falls into and use the corresponding expression from the piecewise function.

Front

What does the expression 4f(-1) - f(6) - 2f(-6) represent?

Back

It represents a combination of evaluations of the piecewise function at different points, which can be calculated to find a single numerical result.

Front

How is the earnings calculation for the house painter structured as a piecewise function?

Back

The earnings are calculated based on different hourly rates for different ranges of hours worked: $12/hour for the first 40 hours, $18/hour for the next 10 hours, and $24/hour for any hours beyond that.

Front

What is the total earnings for a painter who works 70 hours?

Back

The total earnings for a painter who works 70 hours is $1140.