Question

Find numbers a and b so that f is continuous at every point.
16, x<-5
f(x)={ax+b, -5< or equal to x < or equal to 3
-8, x>3

Answer 1

\[\Large\rm f(x)=\cases{16, & x<-5\\ \Large \rm ax+b, &-5$\le$x$\le$3\\ \Large\rm -8, &x>3}\]So we have a piece-wise thing? Hmm

Answer 2

yeah that's what I was trying to write out

Answer 3

any ideas?

Answer 4

So here is the top and bottom part of our piece-wise

Answer 5

We need a linear function in the middle that connects the points.

Answer 6

Notice, that when this is true, the line y=16, and y=ax+b are `equal at x=-5`, do you see that?

Answer 7

Err wait wait wait.. sorry.
I should be careful how I say that.

Answer 8

The y=16 doesn't have that point because of the strict inequality.
So I guess we need to `approach the point` using limits.

You've learned about limits? :o

Answer 9

FWPPPP where you at :U

Answer 10

sorry I'm back

Answer 11

yeah I know about limits

Answer 12

that's what this problems is part of, a limits lesson

Answer 13

So as we travel along these different curves,
from the left and right,
we can see that they're approaching the same value, x=-5, yes?