16Hit1600
Advanced MathVery hardy-coordinate of a hole in a rational graph

Advanced Math practice question

The function r is defined by r(x) = (x² − 1)/(x − 1) for x ≠ 1. In the xy-plane, the graph of y = r(x) is a line with a single point missing. What is the y-coordinate of the missing point?

Answer: 2

For x ≠ 1, r(x) = x + 1. The missing point is at x = 1, where the line would give y = 2.

Common wrong answers

If you answered 0
0 comes from evaluating x² − 1 at x = 1 without simplifying first.
If you answered 1
1 is the x-coordinate of the missing point.
If you answered -1
−1 comes from a sign error in x + 1.

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