# How do you find the constant a so that the function is continuous on the entire real line given #f(x)=4, #x <= -1#, ax +b, -1< x <1 and 6, #x>=1#?

##### 1 Answer

We have

#### Explanation:

We want to find

Strictly speaking we want to find

Just think about what we know so far, and how it would look:

So for the mid interval we need a straight line passing through

This line would have the following gradient:

Hopefully you could also establish that by inspection!

So our required line passes through

Which we can graph to confirm

Hence, we have