SOLUTION: The graph of the equation y = 10^x lies entirely in Quadrants

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Question 277895: The graph of the equation y = 10^x lies entirely in Quadrants
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Each quadrant represents a certain combination of values for x and y:
                  x        y
Quadrant I     Positive  Positive
Quadrant II    Negative  Positive
Quadrant III   Negative  Negative
Quadrant IV    Positive  Negative

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.

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.

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

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.