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anonymous

  • one year ago

Your friend hands you a graph of the engine power statistics of a race car. He says, “I know this graph is f(x) = –3(x + 4)6 – 8 but I can’t remember how it is related to the graph of x6.” Explain to your friend how the graph f(x) is a translation of the graph x6.

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  1. anonymous
    • one year ago
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    Parent function: \[f(x)=x^6\] |dw:1435434334236:dw|

  2. anonymous
    • one year ago
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    let's start with the number in the "h" space. How much has the graph shifted and in which direction?

  3. anonymous
    • one year ago
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    4, and to the right? or would it be left because there is a - sign next to it?

  4. anonymous
    • one year ago
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    4 to the left, and yes because of the - sign

  5. anonymous
    • one year ago
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    now look at a. we know it was reflected because of the - sign outside. By what factor was it stretched?

  6. anonymous
    • one year ago
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    I'm not sure what that means exactly..

  7. anonymous
    • one year ago
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  8. anonymous
    • one year ago
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    Look at the graph. the red one is the original x^6. The blue one has been stretched vertically by a factor of 3, meaning it increases 3 times faster than x^6. The green one has been compressed by a factor of 1/3, meaning it only increases at a third as fast as x^6.

  9. anonymous
    • one year ago
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    does that make sense?

  10. anonymous
    • one year ago
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    Yes!

  11. anonymous
    • one year ago
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    ok. and then the last thing is the vertical shift

  12. anonymous
    • one year ago
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    what do you think, up or down?

  13. anonymous
    • one year ago
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    Down?

  14. anonymous
    • one year ago
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    yes!

  15. anonymous
    • one year ago
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    Awesome! So is that it? How should I word this?

  16. anonymous
    • one year ago
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    that's it. you should go in the order we did it, order of operations style. It was shifted left by 4, reflected over the x-axis, stretched by a factor of 3, and shifted down by 8.

  17. anonymous
    • one year ago
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    see this for more info http://www.regentsprep.org/regents/math/algtrig/atp9/funclesson1.htm

  18. anonymous
    • one year ago
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    Thank you so much for your help!

  19. anonymous
    • one year ago
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    you're welcome

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