Question

Find numbers a and b, so that f is continuous at every point.

f(x)= 16, when x is less than -5
ax+b, when x is greater than or equal to -5 and less than or equal to 3
-8, when x is greater than 3

Answer 1

If you make a graph, you get three different line segments.
To be a continuous function, these segments must be joined at x=-5 and x=3.

The part ax+b has to go through the endpoints of the other lines, so through (-5,16) and (3,-8).

In my example this is not the case :\

So if you have y=ax+b, just put the x and y of both the points in and solve the system for a and b.

Answer 2

how do you solve to two variables at once?

Answer 3

Like this:
Put (-5, 16) in: 16 = -5a + b
Put (3, -8) in: -8 = 3a + b

Can you solve this system of equations?

Answer 4

yes, I see it now. that was a duh moment. Thank you so much!

Answer 5

YW!