Determine g(x+a)-g(x)

Question

g(x)=-x^2-x

g(x+a)-g(x)=??

My online class did not go over this part so I’m a little confused, thanks!

Answer 1

This is going to be a plug-and-chug kind of situation, where you have to keep track of your x's and your a's.

First, let's find g(x+a). We know that g(x) = x² - x, but it might be easier to think of it generally as this:

g(input) = (input)² - (input). This way, we can think of our input as x + a, and have this:

g(x+a) = (x+a)² - (x+a) = x² + 2ax + a² - x - a = x² + 2ax - x + a² - a = x² + (2a - 1)x + (a² - a)

Now that you know g(x + a), you can subtract g(x), which is just x² - x from what we got above.

Hope that helps! Let me know if you have any further questions.