Consider f(x)=x^2/(x^2+a), a>0. Determine the effect on the graph of f if a is varied.

Question

A. Each y value is multiplied by a
B. As a increases, the vertical tangent lines move further from the origin
C. The graph of the curve is shifted sqrt(a) units to the left.
D. As a increases, the curve approaches its asymptote more slowly
E. None of these

Answer 1

have some fun at Wolfram .
Change the value of the constant to see what effect it has on your graph.
http://www.wolframalpha.com/input/?i=plot+y+%3D+%3Dx%5E2%2F%28x%5E2%2B5%29+

It appears as if the shape does not change, but if you look at the scale , what Wolfram is doing is to change the scale on the x-axis

Answer 2

Or, you can plot multiple curves to compare them:

http://www.wolframalpha.com/input/?i=plot+y+%3D+%3Dx^2%2F%28x^2%2B5%29+%2C+y%3Dx^2%2F%28x^2%2B20%29