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anonymous

  • one year ago

The graph of f(x) = 2^x + 4 shifts six units to the right when it is replaced with the graph of f(x) = 2^x - k. What is the value of k?

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  1. anonymous
    • one year ago
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    2 4 6 10

  2. anonymous
    • one year ago
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    @jim_thompson5910 do you think you could help?

  3. jim_thompson5910
    • one year ago
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    the x+4 is all in the exponent?

  4. anonymous
    • one year ago
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    yep

  5. jim_thompson5910
    • one year ago
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    so is x-k ?

  6. anonymous
    • one year ago
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    yep

  7. jim_thompson5910
    • one year ago
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    to shift f(x) 6 units to the left, we replace every x with x+6

  8. anonymous
    • one year ago
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    ok

  9. anonymous
    • one year ago
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    so it would be x+6+4?

  10. jim_thompson5910
    • one year ago
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    Correct \[\Large f(x) = 2^{x+4}\] \[\Large f(x+6) = 2^{x+6+4}\]

  11. jim_thompson5910
    • one year ago
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    simplify x+6+4 and compare it to x-k to figure out what k would be

  12. anonymous
    • one year ago
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    so it'll be x+10

  13. anonymous
    • one year ago
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    so k=10?

  14. jim_thompson5910
    • one year ago
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    x+10 x-k k = ???

  15. jim_thompson5910
    • one year ago
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    it might help to rewrite x+10 as x-(-10)

  16. anonymous
    • one year ago
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    im confused

  17. anonymous
    • one year ago
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    wait would it be 10-k?

  18. jim_thompson5910
    • one year ago
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    \[\Large x + 10\\ \Large x - (-10)\\ \Large x - (\color{red}{-10})\\ \Large x - \color{red}{k} \] So k = -10

  19. anonymous
    • one year ago
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    but there isnt a -10 as an answer

  20. jim_thompson5910
    • one year ago
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    oh I went the wrong direction. It's to the right, so x gets replaced with x-6

  21. anonymous
    • one year ago
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    so it would be x+2?

  22. jim_thompson5910
    • one year ago
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    f(x) = 2^(x+4) f(x-6) = 2^(x-6+4) f(x-6) = 2^(x-2) so k = 2

  23. jim_thompson5910
    • one year ago
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    x-2 actually

  24. anonymous
    • one year ago
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    thank you

  25. anonymous
    • one year ago
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    i got it right :D

  26. anonymous
    • one year ago
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    thank you so much

  27. jim_thompson5910
    • one year ago
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    np

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