1954 AMC 12 Problem 17

Attempt Problem 17 of the 1954 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1954 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

17.

The graph of the function

f(x)=2x^3-7

goes:

up to the right and down to the left

down to the right and up to the left

up to the right and up to the left

down to the right and down to the left

none of these ways

The constant

-7

shifts the graph vertically but does not change its end behavior

A positive odd-degree leading term tends to

+\infty

on the right and

-\infty

on the left

The leading term

2x^3

controls the end behavior. As

x

tends to

+\infty,

f(x)

tends to

+\infty;

x

tends to

-\infty,

f(x)

tends to

-\infty.

Thus the graph goes up to the right and down to the left.

The correct answer is A.

Problem 17 in other years