Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "1954 AHSME Problems/Problem 17"

(→‎Solution 1)
(→‎Solution 1)
Line 12: Line 12:
 
<math>\lim_{x\to-\infty} f(x)=-\infty</math>.  
 
<math>\lim_{x\to-\infty} f(x)=-\infty</math>.  
  
−
This means it goes up and the right, and down and to the left. <math>\boxed{(\boxed{A})}</math>
+
This means it goes up and the right, and down and to the left. <math>\boxed{(\textbf{A})}</math>

Revision as of 19:15, 14 April 2016

Problem 17

The graph of the function $f(x) = 2x^3 - 7$ goes:

$\textbf{(A)}\ \text{up to the right and down to the left} \\ \textbf{(B)}\ \text{down to the right and up to the left}\\ \textbf{(C)}\ \text{up to the right and up to the left}\\ \textbf{(D)}\ \text{down to the right and down to the left}\\ \textbf{(E)}\ \text{none of these ways.}$

Solution 1

What the question is basically asking, is the limit as the function goes to each end of infinity:

$\lim_{x\to\infty} f(x)=\infty$

$\lim_{x\to-\infty} f(x)=-\infty$.

This means it goes up and the right, and down and to the left. $\boxed{(\textbf{A})}$

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1954_AHSME_Problems/Problem_17&oldid=78061"