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

Question

This is a question from my Cal 1 study guide. 

 

f(x)=

       {x²           when x<-5

       {ax+b     when -5≤x≤-4

       {x+20     when x>-4

 

The answers are a=-9 and b=-20. 

 

I plugged in lim(x²) when x approaches -5^- and got 25 and did the same for  lim(x+20) when x approaches 4⁺ and got 16 where but didn't know how to solve for a or b. Can anybody help me with this question? Thanks. 

Answer 1

Here's what do do:

set (-5)² = -5a + b for continuity at x=-5;

set -4+20 = -4a+b for continuity at x=-4.

 

So this is a system of two equations; solve for a & b.

Answer 2

x² must connect to ax+b at x=-5,  and ax+b must connect to

x+20 at x=-4

 

So for     x=-5:    (-5)²=a(-5)+b       or  -5a+b=25

and for   x=-4:    a(-4)+b=-4+20    or  -4a+b=16

Solve these together to get  a=-9  and b=-20