Difference between revisions of "1950 AHSME Problems/Problem 44"
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The graph of <math> y\equal{}\log x</math> | The graph of <math> y\equal{}\log x</math> | ||
| − | <math>\textbf{(A)}\text{Cuts the }y\text{-axis} \qquad\\ | + | <math>\textbf{(A)}\ \text{Cuts the }y\text{-axis} \qquad\\ |
\textbf{(B)}\ \text{Cuts all lines perpendicular to the }x\text{-axis} \qquad\\ | \textbf{(B)}\ \text{Cuts all lines perpendicular to the }x\text{-axis} \qquad\\ | ||
\textbf{(C)}\ \text{Cuts the }x\text{-axis} \qquad\\ | \textbf{(C)}\ \text{Cuts the }x\text{-axis} \qquad\\ | ||
\textbf{(D)}\ \text{Cuts neither axis} \qquad\\ | \textbf{(D)}\ \text{Cuts neither axis} \qquad\\ | ||
\textbf{(E)}\ \text{Cuts all circles whose center is at the origin}</math> | \textbf{(E)}\ \text{Cuts all circles whose center is at the origin}</math> | ||
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== Solution == | == Solution == | ||
The domain of <math>\log x</math> is the set of all positive reals, so the graph of <math>y=\log x</math> clearly doesn't cut the <math>y</math>-axis. It therefore doesn't cut every line perpendicular to the <math>x</math>-axis. It does however cut the <math>x</math>-axis at <math>(1,0)</math>. In addition, if one examines the graph of <math>y=\log x</math>, one can clearly see that there are many circles centered at the origin that do not intersect the graph of <math>y=\log x</math>. Therefore the answer is <math>\boxed{\textbf{(C)}\ \text{Cuts the }x\text{-axis}}</math>. | The domain of <math>\log x</math> is the set of all positive reals, so the graph of <math>y=\log x</math> clearly doesn't cut the <math>y</math>-axis. It therefore doesn't cut every line perpendicular to the <math>x</math>-axis. It does however cut the <math>x</math>-axis at <math>(1,0)</math>. In addition, if one examines the graph of <math>y=\log x</math>, one can clearly see that there are many circles centered at the origin that do not intersect the graph of <math>y=\log x</math>. Therefore the answer is <math>\boxed{\textbf{(C)}\ \text{Cuts the }x\text{-axis}}</math>. | ||
Revision as of 00:19, 2 October 2014
Problem
The graph of $y\equal{}\log x$ (Error compiling LaTeX. Unknown error_msg)
Solution
The domain of 
is the set of all positive reals, so the graph of 
clearly doesn't cut the 
-axis. It therefore doesn't cut every line perpendicular to the 
-axis. It does however cut the -axis at 
. In addition, if one examines the graph of , one can clearly see that there are many circles centered at the origin that do not intersect the graph of . Therefore the answer is 
.
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See Also
| 1950 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 43 |
Followed by Problem 45 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
