Question

Make it continuous!

Answer 1

@Empty Hey there! are you available? :)

Answer 2

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

Answer 3

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

Answer 4

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!

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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 :)

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

yup

Answer 13

b= 4/5

Answer 14

a = 13/20 ? o.o

Answer 15

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

Answer 16

how did you solve them ?

because i get a different answer...

Answer 17

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

Answer 18

Oh. then b = 13/2

Answer 19

\(\huge \checkmark \)

Answer 20

Lol. Thaaank you. Sorry about my brain deadness.

Answer 21

no problem, welcome ^_^