I'm sorry I used a picture for the function here. I've forgotten the name of the type of function that changes behavior depending on the value of $x$, and I'm not sure how to use the math notation functionality here to display it in the form it's normally drawn in.
$$ f(x)=\left\{\begin{array}{ll}{x^{2}-7,} & {x \leq c} \\ {8 x-23,} & {x>c}\end{array}\right. $$
I need to find the value of $c$ such that $f(x)$ is continuous.
The reason I'm having trouble is because I don't know of a good way to find $c$. Could somebody please help me out?
All you need to do is compare the two cases at $x = c$. In other words, $f$ will be continuous at $x = c$ if $c$ satisfies $$c^2 - 7 = 8c - 23.$$