Question

Peter played his favorite video game for 10 hours last week. Today Peter's parents restricted him to 5 hours each week for the next 8 weeks. Create the function, f(x), that models Peter's total video game time and explain what each number in the situation represents graphically, using complete sentences.

Answer 1

@myininaya

Answer 2

@marigirl I feel bad for asking you so many questions :(

Answer 3

@theEric

Answer 4

Hi! I can help intermittently! If there's something I say that you don't understand, just let me know.

Do you know what the independent variable will be?

Answer 5

the 8 weeks?

Answer 6

Yep! Well, it mentions last week, too. So we should probably consider all 9 weeks.
The independent variable, then, will be "weeks."

Since we're writing your function as \(f(x)\) because the problem says so, we will say that \(x\) stands for the week number. How does that sound?

Answer 7

Fantastic

Answer 8

Okay! So, we'll say that "today" is week 0. I changed my mind about including last week. I mean, I don't think that's what the problem is going for.

So, at \(x=0\), meaning zero weeks have passed, how many hours total have been played.

Answer 9

if we have 0 weeks. then 0 hours?

Answer 10

Nope! Good guess, but Peter has some hours under his belt already.

Answer 11

so 10 from last week?

Answer 12

Right! So, at \(x=0\), we see that \(f(0)=10\).
Do you know the name for the value of the function when \(x=0\)? Starts with an 'i.'

Answer 13

inverse?

Answer 14

Close! Not in meaning, but the spelling is close.

interc---

Answer 15

intercept?

Answer 16

You're right! :)
So, if you have
\(f(x)=mx+b\)
for a line, where is the intercept? (Hint, set \(x=0\))

Answer 17

m(0)+b
=b

Answer 18

Right! The intercept is \(10\ \rm hours\) and \(b\) in the equation. So, when we finish, make sure you point out that the number "10" indicates the total hours played at the start of today, the "intercept." "Intercept will probably be a key word.

Answer 19

Okay

Answer 20

@david111

Answer 21

??

Answer 22

@theEric

Answer 23

5 hours per week, what does that tell you?

Answer 24

x?

Answer 25

i really have no idea

Answer 26

every one week, you gain five hours. If you have some scratch paper, it might help you see the picture by plotting this! Remember, start at \(f(0)=10\) !