Questions about the world of GRE Math from other sources and general math related questions.
jurdi.sarah09
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Graphs of Absolute Value

by jurdi.sarah09 Mon Aug 08, 2016 10:28 pm

Could you please go over how to determine the domain, y-intercept, x-intercepts, and vertex of f(x) = |x| and of f(x) = x + |x|?
tommywallach
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Re: Graphs of Absolute Value

by tommywallach Thu Aug 18, 2016 4:44 pm

I've never seen a GRE question ask for the vertex or the domain of a function, so you can just forget those terms. Actually, I've never seen a parabola question tested on the real GRE at all.

That said, you need to know that the x-intercepts are where y = 0 (or in the case of a function, whenever f(x) = 0). The y-intercepts are where x=0. So all you have to do is solve.

f(x) = |x|

f(x) = 0 here when x = 0, and vice versa, so this thing hits the origin. There are your intercepts.

and of f(x) = x + |x|?

f(x) = 0 here when x = 0 OR whenever x is positive. So this just runs along the x-axis and then turns upwards. Y-intercept remains 0. In my experience, this question simply wouldn't be asked, because it doesn't really have an x-intercept (or it has an infinite number).

-t