Difference between revisions of "1992 AHSME Problems/Problem 14"
(Created page with "== Problem == Which of the following equations have the same graph? <math>I.\quad y=x-2 \qquad II.\quad y=\frac{x^2-4}{x+2}\qquad III.\quad (x+2)y=x^2-4</math> <math>\text{(A)...") |
(→Solution: added solution) |
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== Solution == | == Solution == | ||
| − | <math> | + | The equations differ at <math>x=-2</math>. The graph of <math>I</math> would contain the point <math>(-2, -4)</math>; <math>-2</math> is undefined in the graph of <math>II</math> because it gives a denominator of <math>0</math>; and the graph of <math>III</math> contains the whole the vertical line <math>x = -2</math> as for any <math>y</math> value, the equation still satisfies <math>0 = 0</math>. So the answer is <math>{E}</math>. |
== See also == | == See also == | ||
Latest revision as of 21:45, 18 January 2018
Problem
Which of the following equations have the same graph?
Solution
The equations differ at 
. The graph of 
would contain the point 
; 
is undefined in the graph of 
because it gives a denominator of 
; and the graph of 
contains the whole the vertical line 
as for any 
value, the equation still satisfies 
. So the answer is 
.
See also
| 1992 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
