Question

Let f be defined as follows:
h(x)=

-x-3 for x greater than or equal to 1

ax+b for -2<x<1

x(squared) for x less than or equal to -2

Find the values of "a" and "b" that make h(x) continous.

I'm a bit stumped on how to go about solving this one. Help would be greatly appreciated. :)

Answer 1

look at the transition points, they should be the same.

when x = 1
h(x) = -x - 3 = -1-3 = -4
h(1) = a + b
so a+b = -4

h(-2) for ax+b = -2a+b
h(-2) for x^2 = 4
so -2a + b = 4

a+b = -4
-2a +b = 4
subtract:
3a = -8
a = -8/3,
back in a+b= -4
-8/3+b = 4
b = 20/3

a = -8/3 , b = 20/3