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

Question

f(x)=

    {x²      when x<-3

    {ax+b   when -3≤x≤4

    {x+2   when x>4

Answer 1

The three pieces of f(x) are continuous; therefore, you can write a pair of simultaneous linear equations in a and b, the solution of which is your answer.

At x=-3, 9=-3a+b and

at x=4, 6=4a+b.