Question

Compare the three functions.

f(x) = 3x
g(x) = 3x2
h(x) = 6x


Which of the statements is true?
A. As x approaches positive infinity, g(x) exceeds f(x) and h(x).
B. As x approaches positive infinity, f(x) converges with g(x).
C. As x approaches positive infinity, f(x) exceeds g(x) and h(x).
D. As x approaches positive infinity, h(x) exceeds f(x) and g(x).

Answer 1

As x approaches +inf, g(x) clearly exceeds both f(x) and h(x). Why not graph all 3 functions to verify this? g(x) is a parabola, whereas the other 2 are str. lines.

Answer 2

Remark
With a question like this one, be very careful. The first thing to do is make a graph. That is done below.

f(x) is read
g(x) is blue
h(x) is green

I have actually made 2 graphs. The left one is to show the detail around the origin. the second one is with an axis that goes quite a bit further out in the x and y directions.

Discussion of answers
B is not correct. The graphs seem to converge when y = 12. After that g(x) is off to the races and it gets larger and larger values as x increases.

C Which color is on top? Which color goes up the most quickly. It isn't the red one. C is False.

D Nothing exceeds g(x) once it gets going.

Answer: A <<<<<<