Question

Jan works from 30 to 40 hours per week during the summer. She earns $12.00 per hour. Her friend Rachel also has a job. Rachel's pay for t hours is given by the function r(t) = 11t, where 20 ≤ t ≤ 30. Find the domain and range of each function. Compare their hourly wages and the amount they earn per week. j(t) domain: ≤ t ≤ j(t) range: ≤ j(t) ≤ r(t) domain: ≤ t ≤ r(t) range: ≤ r(t) ≤ (select) earns more per hour than (select) . Jan earns from $ to $ per week and Rachel earns from $ to $ per week.

Answer 1

The domain of f(x) is 30 ≤ x ≤ 40 and range is 360 ≤ f(x) ≤ 480

The domain of r(t) is 20 ≤ t ≤ 30 and the range is 220 ≤ r(t) ≤ 330.

We see that Jan earns between 360usd to 480usd weekly while Rachel earns between 220usd to 330usd weekly.

Explanation:

Since Jan earns 12usd per hour. This means her pay will be f(x) = 12x where 30 ≤ x ≤ 40, this means x is the number or hours worked. The number of hours worked determines the pay.

Rachel's pay is given by r(t) = 11t, where 20 ≤ t ≤ 30. This means that t is the number of hours worked and the pay depends on the number of hours worked.

The domain of f(x) is 30 ≤ x ≤ 40 because this are the values x can assume in this function.

The range will therefore be 12 x 30 ≤ f(x) ≤ 12 x 40, because f(x) = 12x, therefore the lowest range is 12 x 30 and the highest is 12 x 40. So we have:

360 ≤ f(x) ≤ 480.

Similarly, the domain of r(t) is 20 ≤ t ≤ 30. And the range is 11 x 20 ≤ r(t) ≤ 11 x 30 because r(t) = 11t. So we have 220 ≤ r(t) ≤ 330 as the range.

Comparing their hourly weekly rate. We see that Jan earns between 360usd to 480usd weekly while Rachel earns between 220usd to 330usd weekly.