Piecewise Function Word Problems

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 calculate earnings using a piecewise function?

Back

To calculate earnings, identify the intervals of hours worked and apply the corresponding rate for each interval.

Front

What is the formula for calculating the total cost of renting video games if the first five games cost $3 each and subsequent games cost $1?

Back

f(x) = 25 - 3x for 0 ≤ x ≤ 5; f(x) = 15 - x for 6 ≤ x ≤ 10.

Front

What does the domain of a piecewise function represent?

Back

The domain represents the set of input values (e.g., hours worked, weight of cans) for which the function is defined.

Front

What does the range of a piecewise function represent?

Back

The range represents the set of output values (e.g., total earnings, total cost) that the function can produce.

Front

How do you determine the total earnings for a painter who charges different rates for different hours worked?

Back

Calculate earnings for each interval separately and then sum them up.

Front

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

Back

Breakpoints indicate where the function changes its rule or formula based on the input value.

Front

If a function is defined as f(x) = 7h for 0 ≤ h ≤ 40, what does this mean?

Back

It means that for any hours worked (h) between 0 and 40, the pay is calculated at $7 per hour.

Front

What is the formula for calculating taxes owed using a piecewise function?

Back

The formula varies based on income brackets, with different rates applied to different income ranges.

Front

How do you express a piecewise function for a job that pays overtime?

Back

Define one formula for regular hours and another for overtime hours, indicating the conditions for each.