Question

problems 4–7: rafael earns $10.50 per hour helping his neighbor with chores.

1. is the amount he earns a function of the number of hours he works? explain your thinking.
2. is the number of hours he works a function of the amount he earns? explain your thinking.
3. write an equation that describes the situation. use x to represent the independent variable and y to represent the dependent variable.
4. how much will rafael earn if he works 3 hours each weekday next week? show or explain your thinking.

Explanation:

Step1: Answer Q4: Define function check

A function maps each input to exactly one output. Here, each number of hours (input) leads to exactly one earned amount (output, calculated as $10.50 \times$ hours). So this is a function.

Step2: Answer Q5: Reverse function check

For the reverse, one earned amount (input) could correspond to only one number of hours (since hours = $\frac{\text{earned amount}}{10.50}$). Each input maps to exactly one output, so this is a function.

Step3: Q6: Define variables & equation

Let $x$ = hours worked (independent), $y$ = total earnings (dependent). Total earnings equal hourly rate times hours:
$y = 10.50x$

Step4: Q7: Calculate total hours & earnings

There are 5 weekdays. Total hours: $5 \times 3 = 15$ hours.
Earnings: $y = 10.50 \times 15$

Answer:

1. For Question 4: Yes, it is a function. Each number of hours worked (input) results in exactly one unique amount of earnings (output), since earnings are fixed at $10.50 per hour.
2. For Question 5: Yes, it is a function. Each amount of earnings (input) corresponds to exactly one unique number of hours worked (output), as hours can be calculated by dividing total earnings by the hourly rate of $10.50.
3. For Question 6: $y = 10.50x$
4. For Question 7: $\$157.50$