Question

An accountant charges an initial fee of $100 plus a rate of $40 per hour. The function that shows the total fees charged is f(x) = 40x + 100. How would the graph of the function change if the accountant raised his rate to $45 per hour?

Answer 1

The graph of the function f(x) = 40x + 100 would change to f(x) = 45x + 100 if the accountant raised his rate to $45 per hour. The new function would have a steeper slope, resulting in higher fees for the same number of hours.

Step-by-step explanation:

The graph of the function f(x) = 40x + 100 shows the total fees charged by the accountant, where x represents the number of hours. To find out how the graph would change if the accountant raised his rate to $45 per hour, we can replace the coefficient of x in the function with 45. The new function would be f(x) = 45x + 100.

This change would result in a steeper slope for the graph. The cost per hour of the accountant's services would be higher, so the total fees charged would increase at a faster rate.

For example, if the accountant worked for 2 hours, the total fees charged would be f(2) = 45(2) + 100 = $190. If the rate was still $40 per hour, the total fees charged would have been f(2) = 40(2) + 100 = $180. The increase in rate would lead to a higher fee for the same number of hours.