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Student Question on ETS Material: Graphs of Absolute Value Functions

Here’s a question that one of our students sent in– ask and you shall receive! 🙂

“Hello team Magoosh. First I’d like to say I love this site, I’ve learned so much! I’m posting a question about a certain math problem I found on the official ETS website. I tried to solve it and got it wrong. Below the math problem is described:

The figure above shows the graph of a function f, defined by f(x)=|2x|+4 for all numbers x. For which of the following functions g defined for all numbers x does the graph of g intersect the graph of f ?

A graph depicted the f(x) equation.

The answer ended up being g(x)=3x-2

…do you think you post a video as to how and why this is the answer?

– James”



You may also want to check out absolute value basics. Let us know if you have any questions about this (or anything else GRE-related!).


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6 Responses to Student Question on ETS Material: Graphs of Absolute Value Functions

  1. Vaishnavi March 4, 2014 at 9:48 am #


    Would you please explain why the answers can’t be g(x) = x-2 or g(x)= x + 3? Thank you!

  2. Niraj June 9, 2013 at 12:20 am #

    I still don’t understand why the answer can’t be D: y=2x+3? If you graph this on the graph, doesn’t it intersect y=2x+4? Because with y=2x+3, it starts at 3 and it goes up 2 and over 1 so just the first time it does that doesn’t it cross the origin of the absolute value graph? Does crossing the origin not mean intersect?

    • Chris Lele
      Chris Lele June 10, 2013 at 12:38 pm #

      Hi Niraj,

      Since y = 2x+3 and y = 2x+4 both have the same slopes they will parallel to each other, and thus will never intersect. y = 2x+4 will be one point “higher” than y = 2x+3.

      Hope that helps!

      • MM December 12, 2017 at 10:43 pm #


  3. James February 9, 2012 at 5:08 pm #

    Hey, I appreciate the explanation, makes perfect sense now!

    • Chris Lele
      Chris February 10, 2012 at 11:48 am #

      Great! I’m happy it made things clear

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