Question

Ariel charges $8 per hour as a babysitter. She rounds every fraction of an hour up to the next half-hour. Draw a graph to represent Ariel’s total earnings y after x hours.

Answer 1

The total earnings of Ariel as a babysitter can be represented using a piecewise function. For whole hours, she earns $8 per hour, and for fractional hours, she rounds up to the next half-hour.

Step-by-step explanation:

To represent Ariel's total earnings after x hours as a babysitter, we can use a piecewise function. Let's define the function as follows:

y = 8x, for x = 0, 1, 2, 3, ...

y = 8 * ceil(x), for x = 0.5, 1.5, 2.5, ...

This means that for whole hours (x = 0, 1, 2, 3, ...), Ariel earns $8 per hour. But for fractional hours (x = 0.5, 1.5, 2.5, ...), Ariel rounds up the fraction to the next half-hour and earns $8 for that portion as well.