Question

Find the values for a and b such that f(x) is continuous on the interval 0 < or = to x < or = to 13.

{ 2x^2, 0 < or = to x < or = to 3
f(x) = { ax + 3, 3 < or = to x < or = to 7
{ b, 7 < or = to x < or = to 13

Can someone explain? Am I suppose to find the x, a, and b that would make all three sets equal to the same number?

Correction:

f(x) = { 2x^2, 0 < or = to x < 3
.......{ ax + 3, 3 < or = to x < 7
.......{ b, 7 < or = to x < or = to 13

the ....... is to align them, sorry.

If it is continous, then

2x^2= ax+3 at x=3 put x=3, and solve for a.

And, b= ax+3 at x=7, solve for b

Thank you, bobpursley! I didn't know that that is what they meant by continuous.

So a=5 and b=38?