## 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)

1. anonymous

@JoannaBlackwelder

2. anonymous

@triciaal

3. zepdrix

$\large\rm \color{royalblue}{a(x) = 3x + 10},\qquad \color{orangered}{b(x) = 2x − 8}$ $\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

5x+2?

5. zepdrix

Yay good job! That takes care of part A.

6. anonymous

:}

7. zepdrix

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

(3x+10)(2x+−8) =(3x)(2x)+(3x)(−8)+(10)(2x)+(10)(−8) =6x2−24x+20x−80 =6x2−4x−80

9. anonymous

Correct?

10. zepdrix

Ooo looks good! :O

11. zepdrix

How bout part C, the composition. Having any trouble with that one?

12. anonymous

Yes thats actually the one i am confused on >_<

13. zepdrix

$\large\rm a(\color{#DD4747}{x}) = 3\color{#DD4747}{x} + 10$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

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

15. zepdrix

$\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

=(3)(2x)+(3)(−8)+10 =6x+−24+10 =6x+−24+10 =(6x)+(−24+10) =6x+−14

17. zepdrix

yay good job!

18. anonymous

i need help on part A!!!

19. anonymous

@enchanted_bubbles

20. anonymous

@zeddrix

21. anonymous

@zepdrix

22. zepdrix

Then scroll up and read silly! :D

23. zepdrix

Notice the colors

24. zepdrix

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 = ?