1955 AMC 12 Problem 49

Question

The graphs of

y=\dfrac{x^2-4}{x-2}

and

y=2x

intersect in:

one point whose abscissa is

2

one point whose abscissa is

0

no points

two distinct points

two identical points

Factor

x^2-4

, but keep the original restriction

x\ne2

Compare the algebraic intersection of the simplified lines with that domain restriction

For

x\ne2,

\frac{x^2-4}{x-2}=x+2.

The lines

y=x+2

and

y=2x

would meet at

x=2,\ y=4.

But

x=2

is excluded from the original rational function, so that point is a hole and there is no intersection.

Thus, the correct answer is C.

Problem 49 in other years