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- Babynini

Make it continuous!

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- Babynini

Make it continuous!

- jamiebookeater

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- Babynini

- Babynini

@Empty Hey there! are you available? :)

- Empty

Heyo, alright so any ideas on how to make this continuous?

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- Babynini

Setting two of the equations to equal each other and then subbing a and b in

- Empty

Yeah you're on the right track, what we need to do to make the function continuous is have their heights match up at the same value of x. In order to do that, we take the first equation and set it equal to the second equation and plug in x=2 since at that point they need the same height.
Similarly you will make the second and third equal and plug in the x value there to make them equal.
Then you have two equations and two unknowns to solve for, the values of a and b that make your function continuous!

- Babynini

Yay!!
So part a after plugging 2 in where x is:
4=4a-2b+3?

- Babynini

The first two simplify to: 1=4a-2b

- Babynini

Second two simplify to: 5a=3b+5

- hartnn

when you plug in 3,
9 a - 3b + 3 = 12 -a + b
10a -4b = 9
how did you get
5a=3b+5
for second two ?
4a -2b = 1 is correct :)

- Babynini

Ah sorry, I accidentally plugged 2 instead of 3 on the last two =.=

- hartnn

thought so...since f(x) to be continuous at x =3,
f(3)- and f(3)+ should be equal.

- Babynini

Ahh, gotcha. So now I solve them for a and b?

- hartnn

yup

- Babynini

b= 4/5

- Babynini

a = 13/20 ? o.o

- Babynini

I don't know how I am getting these weird numbers :/

- hartnn

how did you solve them ?
because i get a different answer...

- hartnn

multiply equation 1 by 2
8a -4b =2
subtract this from equation 2
10a - 4b = 9
- 8a -4b = 2
=================
2a + 0 = 7
a =7/2

- Babynini

Oh. then b = 13/2

- hartnn

\(\huge \checkmark \)

- Babynini

Lol. Thaaank you. Sorry about my brain deadness.

- hartnn

no problem, welcome ^_^

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