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TheJP

  • 8 months ago

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.

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  1. TheJP
    • 8 months ago
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    @myininaya

  2. TheJP
    • 8 months ago
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    @marigirl I feel bad for asking you so many questions :(

  3. TheJP
    • 8 months ago
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    @theEric

  4. theEric
    • 8 months ago
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    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?

  5. TheJP
    • 8 months ago
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    the 8 weeks?

  6. theEric
    • 8 months ago
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    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?

  7. TheJP
    • 8 months ago
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    Fantastic

  8. theEric
    • 8 months ago
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    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.

  9. TheJP
    • 8 months ago
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    if we have 0 weeks. then 0 hours?

  10. theEric
    • 8 months ago
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    Nope! Good guess, but Peter has some hours under his belt already.

  11. TheJP
    • 8 months ago
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    so 10 from last week?

  12. theEric
    • 8 months ago
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    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.'

  13. TheJP
    • 8 months ago
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    inverse?

  14. theEric
    • 8 months ago
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    Close! Not in meaning, but the spelling is close. interc---

  15. TheJP
    • 8 months ago
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    intercept?

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

  17. TheJP
    • 8 months ago
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    m(0)+b =b

  18. theEric
    • 8 months ago
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    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.

  19. TheJP
    • 8 months ago
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    Okay

  20. TheJP
    • 8 months ago
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    @david111

  21. TheJP
    • 8 months ago
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    ??

  22. TheJP
    • 8 months ago
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    @theEric

  23. theEric
    • 8 months ago
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    5 hours per week, what does that tell you?

  24. TheJP
    • 8 months ago
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    x?

  25. TheJP
    • 8 months ago
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    i really have no idea

  26. theEric
    • 8 months ago
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    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 \(f(0)=10\) !

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