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anonymous

  • one year ago

Use the functions a(x) = 3x + 10 and b(x) = 2x − 8 to complete the function operations listed below. Part A: Find (a + b)(x). Show your work. (3 points) Part B: Find (a ⋅ b)(x). Show your work. (3 points) Part C: Find a[b(x)]. Show your work. (4 points)

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  1. anonymous
    • one year ago
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    @JoannaBlackwelder

  2. anonymous
    • one year ago
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    @triciaal

  3. zepdrix
    • one year ago
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    \[\large\rm \color{royalblue}{a(x) = 3x + 10},\qquad \color{orangered}{b(x) = 2x − 8}\] \[\large\rm (a+b)(x)=\color{royalblue}{a(x)}+\color{orangered}{b(x)}\]\[\large\rm (a+b)(x)=\color{royalblue}{3x+10}+\color{orangered}{2x-8}\]Combine like-terms! :)

  4. anonymous
    • one year ago
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    5x+2?

  5. zepdrix
    • one year ago
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    Yay good job! That takes care of part A.

  6. anonymous
    • one year ago
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    :}

  7. zepdrix
    • one year ago
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    For part B, you'll want to put some brackets around your a(x) and b(x) so the multiplication works out properly.\[\large\rm (a\cdot b)(x)=(\color{royalblue}{a(x)})\cdot(\color{orangered}{b(x)})\]\[\large\rm (a\cdot b)(x)=(\color{royalblue}{3x+10})\cdot(\color{orangered}{2x-8})\]

  8. anonymous
    • one year ago
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    (3x+10)(2x+−8) =(3x)(2x)+(3x)(−8)+(10)(2x)+(10)(−8) =6x2−24x+20x−80 =6x2−4x−80

  9. anonymous
    • one year ago
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    Correct?

  10. zepdrix
    • one year ago
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    Ooo looks good! :O

  11. zepdrix
    • one year ago
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    How bout part C, the composition. Having any trouble with that one?

  12. anonymous
    • one year ago
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    Yes thats actually the one i am confused on >_<

  13. zepdrix
    • one year ago
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    \[\large\rm a(\color{#DD4747}{x}) = 3\color{#DD4747}{x} + 10\]We're replacing all of the x's in our function a(x) with another function b(x).\[\large\rm a(\color{#DD4747}{b(x)}) = 3\color{#DD4747}{b(x)} + 10\]

  14. zepdrix
    • one year ago
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    But again, since we have some multiplication going on, let's place brackets around the b(x) before we plug it in.

  15. zepdrix
    • one year ago
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    \[\large\rm a(\color{#DD4747}{b(x)}) = 3(\color{#DD4747}{b(x)}) + 10\]\[\large\rm a(\color{#DD4747}{b(x)}) = 3(\color{#DD4747}{2x-8}) + 10\]

  16. anonymous
    • one year ago
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    =(3)(2x)+(3)(−8)+10 =6x+−24+10 =6x+−24+10 =(6x)+(−24+10) =6x+−14

  17. zepdrix
    • one year ago
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    yay good job!

  18. anonymous
    • one year ago
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    i need help on part A!!!

  19. anonymous
    • one year ago
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    @enchanted_bubbles

  20. anonymous
    • one year ago
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    @zeddrix

  21. anonymous
    • one year ago
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    @zepdrix

  22. zepdrix
    • one year ago
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    Then scroll up and read silly! :D

  23. zepdrix
    • one year ago
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    Notice the colors

  24. zepdrix
    • one year ago
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    Recall that addition is commutative, meaning we can move things around. So \(\large\rm 3x+10+2x-8\) is the same as \(\large\rm 3x+2x+10-8\) Combine your x's. You have 3 of them, and 2 more of them. 3 apples + 2 apples = ?

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