## anonymous one year ago plz help medal + fan + testimonial show all the work ( explain) do not use a calculator for parts 1-4. Let f be the function defined as follows:

1. anonymous

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2. anonymous

1. if a=2 and b=3, is f continuous at x=1? justify your answer. 2. find a relationship between a and b for which f is continuous at x=1. ( Hint: A relationship between a and b just means an equation in a and b. 3. Find a relationship between a and b so that f is continuous at x=2. 4. USe your equations from parts (ii)and(III) to find the values of a and b so that f is continuous at both x=1 and at x=2? 5. Graph the piece function using the values of a and b that you have found. you may graph by hand or use your calculator to graph.

3. Loser66

Any idea?

4. anonymous

no im completely clueless in this! o.o

5. Loser66

1) No, since we don't have x =1 on f(x). (The way they define f(x) excludes 1) 2) if f(x) is continuous at x =1, that is the first part = second part (in f(x) I meant if x =1, then y =2 (for f(x) =3-x) Plug it into the second one ax^2 + bx =y with x =1, y =2 to have the relationship between a and b 3) do the same with the second part and the third part for x =2 That is if x =2, y = 0 (for y = 5x-10) Now we have (2,0) , replace in ax^2+bx =y to get the relationship between them.

6. Loser66

4) combine part 2 and part 3 to solve for a, b. We have 2 equations, 2 unknowns --> the system is solvable. 5) graph, this part is the easiest part. I think you can do it, right?

7. anonymous

huuuuuuhhhhh? o.ohow did you get that?

8. Loser66

You asked "how did I get that?" , right? of course, I got it from the courses I took in the past.

9. anonymous

lol I mean how did you arrive to the answers?

10. Loser66

I don't get what you mean. My logic is all in what I said. Read and you can see how, why and answer.

11. anonymous

ok if I need any more help can I message you

12. anonymous

you got this?

13. anonymous

is there anything you wold like to add?

14. anonymous

i was just wondering if you got the answer the question is just walking you through it step by step

15. anonymous

not really im tryig on my own lol. but I am terrible. even with the steps which I appreciate , I am having a little trouble getting to the answer.

16. anonymous

this is what you do plug in 1 for $$x$$ in both $$3-x$$ and $$ax^2+bx$$ you get $3-1=2$ and $a+b$ setting them equal tells you $a+b=2$

17. anonymous

then plug in $$2$$ in $$ax^2+bx$$ and $$5x-10$$ you get $4a+2b$ and $2\times 2-1=0$ telling you $4a+b=0$

18. anonymous

is this for number one?

19. anonymous

now you have $a+b=2\\ 4a+2b=0$ solve that for $$a$$ and $$b$$ and you are done

20. anonymous

wait do I plug in a+b=2 into 4a+2b=0?

21. anonymous

you solve the "system of equations" just as normal $a+b=2\\ 4a+2b=0$ you can solve it using any method you like (or know)

22. anonymous

ok this is what I get: 4a^2+ 2b^2=2