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

“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.Â Let us know if you have any questions about this (or anything else GRE-related!).

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?

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.

Magoosh blog comment policy: To create the best experience for our readers, we will only approve comments that are relevant to the article, general enough to be helpful to other students, concise, and well-written! ðŸ˜„ Due to the high volume of comments across all of our blogs, we cannot promise that all comments will receive responses from our instructors.

We highly encourage students to help each other out and respond to other students' comments if you can!

If you are a Premium Magoosh student and would like more personalized service from our instructors, you can use the Help tab on the Magoosh dashboard. Thanks!

Hi,

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

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?

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!

Thanks!

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

Great! I’m happy it made things clear