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Kristin Fracchia

ACT Challenge Question 17: Linear Graphs with Discontinuity – Explanation

Magoosh ACT Challenge Question


Math geniuses! Below you’ll find the answer and explanation to our ACT Math Challenge Question of the week. But if you missed our earlier post, take a stab at the following question before you peek below:

ACT Challenge Question 17


The graph shows a function graphed in the standard (x, y) plane. Which of the following could be the equation of the function?


Answer and Explanation

The answer is (D).

The graph clearly has a hole, a point discontinuity, at x = 3. This means that the function cannot be defined at x = 3. It must have (x – 3) in the denominator. On this basis, we can eliminate (A), (C), and (E).

Notice that the graph is identical to the line y = 2x – 3 at every point except for the point discontinuity at x = 3. Also, to get a point discontinuity instead of an asymptote, we need to have a factor of (x – 3) in both the numerator and the denominator. Choice (B) at x = 3 has a zero denominator and a non-zero numerator, which is the condition for a vertical asymptote. We have eliminated the other four answers, so it would seem that (D) is the answer, but let’s verify this.

In order to get a graph that is identical to y = 2x – 3 at every point except for x = 3 and has a point discontinuity at x = 3, we would have to multiply (2x – 3) by (x – 3) over itself.acq17_img3.png

So everything checks out and our answer is (D)!


UPDATE! Here’s a great student answer to this question from Abdul. Love those reasoning skills.

Screen Shot 2015-12-29 at 2.45.03 PM


About Kristin Fracchia

Kristin makes sure Magoosh's blogs are chock-full of awesome, free resources for students preparing for standardized tests. With a PhD from UC Irvine and degrees in Education and English, she’s been working in education since 2004 and has helped students prepare for standardized tests, as well as college and graduate school admissions, since 2007. She enjoys the agonizing bliss of marathon running, backpacking, hot yoga, and esoteric knowledge.

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