# 1992 AHSME Problems/Problem 14

## Problem

Which of the following equations have the same graph? $I.\quad y=x-2 \qquad II.\quad y=\frac{x^2-4}{x+2}\qquad III.\quad (x+2)y=x^2-4$ $\text{(A) I and II only} \quad \text{(B) I and III only} \quad \text{(C) II and III only} \quad \text{(D) I,II,and III} \quad \\ \text{(E) None. All of the equations have different graphs}$

## Solution

The equations differ at $x=-2$. The graph of $I$ would contain the point $(-2, -4)$; $-2$ is undefined in the graph of $II$ because it gives a denominator of $0$; and the graph of $III$ contains the whole the vertical line $x = -2$ as for any $y$ value, the equation still satisfies $0 = 0$. So the answer is ${E}$.

## See also

 1992 AHSME (Problems • Answer Key • Resources) Preceded byProblem 13 Followed byProblem 15 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 All AHSME Problems and Solutions

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