document.write( "Question 277895: The graph of the equation y = 10^x lies entirely in Quadrants \n" ); document.write( "

Algebra.Com's Answer #202383 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
Each quadrant represents a certain combination of values for x and y:
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document.write( "                  x        y\r\n" );
document.write( "Quadrant I     Positive  Positive\r\n" );
document.write( "Quadrant II    Negative  Positive\r\n" );
document.write( "Quadrant III   Negative  Negative\r\n" );
document.write( "Quadrant IV    Positive  Negative\r\n" );
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\n" ); document.write( "So if we can figure out what values x can be and what values y can be, then we can figure out what what quadrants the graph will be in.

\n" ); document.write( "In your equation x is the exponent (of 10). What kinds of numbers can exponents be? Answer: Exponents can be any number (positive, negative, zero, whole numbers, fractions, etc.). So x can be any number.

\n" ); document.write( "In your equation the y is $\"10%5Ex\"$ . What kinds of numbers can powers of 10 be? With some careful thought we should be able to determine that powers of 10 can never be zero or negative. Remember:

A zero exponent of 10 results in 1, not zero: $\"10%5E0+=+1\"$
Negative exponents of 10 do not result in negative answers. For example, $\"10%5E%28-3%29+=+1%2F10%5E3+=+1%2F1000\"$

\n" ); document.write( "So we have found that x can be anything but y has to be positive. In which quadrants are positive y's found? The answer to this question is the answer to your problem. \n" ); document.write( "

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