Hi Mike,

So I can’t understand the answer key explanation for the 131st question in the Extra Practice (PWN 5th edition)

Could you explain how to solve this problem?

For everyone following along at home:

The thing to know here is that the only reason a value wouldn’t be included in the domain of a function like this (a rational function) is that they make the denominator equal zero. So really, this question is asking you to find the zeros of the denominator. You need to solve 0=7x^2-2x-5.

If this were a calculator allowed question, then you would 100% want to just graph it. Unfortunately it is not, which is why the solution in the book instead finds the solutions using the quadratic formula. Since that’s already in the book, though, maybe what it makes most sense here to help clarify that solution is to show it graphically anyway.

Below is the Desmos graph of y=7x^2-2x-5. You can see that y=0 at x=-0.714... and x=1. Those are the values of a and b from the question—those values won’t be in the domain of the function because they make the denominator equal zero.

The question asks for the sum of those values, so you want to add them together: -0.714+1=0.286. Which answer choice gives you that?

It’s not going to be A or C, because we know fractions with 3 on bottom end in 0.333 or 0.666. It won’t be B because \dfrac{12}{7} is greater than 1. By process of elimination then, it must be D.

But again, I’m just going through all this to illustrate what the question is asking for and the thought process to follow to get there. If you really had to do this without a calculator, you’d want to use the quadratic formula like I did in the solution in the book.

Hope this helps!

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