Question 7
Answers:
Jane's Uber business has the function f(x) = 0.10x+5
Joe's Uber business has the function f(x) = 0.20x+4
x is the number of miles, f(x) is the total cost for the customer
Explanation:
Jane charges $5 no matter how many miles are driven. This is the base fee. On top of this base fee, an additional price is charged based on the number of miles driven. If Jane drives 1 mile, then an additional 0.10*1 = 0.10 dollars is added on. If 2 miles are driven, then 0.10*2 = 0.20 dollars is added on. And so on.
In general, an additional 0.10*x dollars is added on the base fee to get the total cost to be 5 + 0.10x which rearranges to 0.10x + 5. That's how I ended up with f(x) = 0.10x + 5
Joe's equation will be constructed in a similar way. His base fee is $4 and you add on 0.20x dollars (since it costs $0.20 per mile for Joe's company). Overall, we get f(x) = 0.20x + 4 for Joe's company.
Note how your teacher is not asking you to solve for x or f(x). If you want, you can replace f(x) with y; however, this isn't in function notation.
Question 8
Answers:
Function for Joseph's plan is: f(x) = 0.10x + 20
Function for Micki's plan is: f(x) = 0.15x + 10
The plans cost the same when 200 text messages are sent
Explanation:
We'll set up the equations in a similar way done in problem 7. We start with $20 as the base fee for Joseph's plan and then add on 0.10x dollars because $0.10 is charged per text message. We have x represent the number of text messages. Joseph's function is therefore f(x) = 0.10x + 20. Similarly, Micki's function is f(x) = 0.15x + 10
Let's replace f(x) with y and we have these two equations: y = 0.10x + 20 and y = 0.15x + 10
Now use substitution to solve for x and y
y = 0.10x + 20
0.15x + 10 = 0.10x + 20 ... y replaced with 0.15x+10
0.15x-0.10x = 20-10
0.05x = 10
x = 10/0.05
x = 200
This means that the two plans cost the same when 200 messages are sent.
Note plugging x = 200 into each f(x) function leads to
f(x) = 0.10x + 20
f(200) = 0.10*200 + 20
f(200) = 20 + 20
f(200) = 40 <<--- it costs Joseph $40 to send 200 messages
and
f(x) = 0.15x + 10
f(200) = 0.15*200 + 10
f(200) = 30 + 10
f(200) = 40 <<--- it costs Micki $40 to send 200 messages
