I'm sorry to come back with another Calculus question, to those of you who see me asking often.

I'm trying to make the following function continuous.

$\displaystyle f(x) = -1 $ if $\displaystyle x <= 0 $

$\displaystyle ax+b$ if $\displaystyle 0 < x < 1$

$\displaystyle 1 $ if $\displaystyle x >= 1$

I've seen simple examples which use limits to find the values but here I believe I would have to use the following limits, which will produce different values.

$\displaystyle \lim_{x \to -1} ax+b = -1$

$\displaystyle \lim_{x \to 1} ax+b = 1$

I honestly don't think this makes any sense.