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.
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.