Question

determine the value of c so that f(x) is continuous on the entire real line when

Answer 1

did you try to sketch the function? basically for your function to be continuous, you must make sure that there are 'no gaps, no holes' when you look at the function. This means that the your function must have the same value at the critical point \(x=-1\) otherwise your function will make a 'jump' and therefore be not continuous.

Use a graphic engine of your choice to confirm this for yourself
i.e. https://www.desmos.com/calculator