Question

Okay well this one is just an example,
I have like, 7 problems I have to do like this, but I need
an explanation as to how to solve it.

F(x)= {x^2, x<-5
ax + b, -5
≤
x
≤
4
x+12, x>4

find the value of a and b or k so that x is continuous

Answer 1

For a function to be continuous, it needs to be smooth, meaning there aren't any sort of kinks or sudden breaks. This means that for a piece-wise function like this to be continuous, the values for every single section has to be the same at the end points of each interval.

In your example, you just need to choose a and b so that when you plug -5 and 4, the output of -5 should match the first part, and the output of 4 matches the 3rd part of the function. Thus a(-5)+b=25 and a(4)+b=16 are the two equations you need to solve. I got a=-1 and b=20.