The function is g(x) = (x^2 - a^2)/(x - a) if x doesn't equal a; and the second part is g(x) = 8 when x = a. The question asks for me to find a specific value for a so that the function might be continuous on the entire real line. I know that each part of the piece-wise function needs to equal the same y-value, in order for their graphs to overlap; and, also, that the limit needs to approach the same value from each side of this point of possible discontinuity. Is that right? I am just not certain how to go about this. Could someone possibly prod me towards the correct route of solving this problem? Thank you.