Geraldine is asked to explain the limits on the range of an exponential equation using the function f(x) = 2x. She makes these two statements:1. As x increases infinitely, the y-values are continually doubled for each single increase in x.2. As x decreases infinitely, the y-values are continually halved for each single decrease in x.
Answer
A
Statement 1 is incorrect because the y-values are increased by 2, not doubled.
B
Statement 2 is incorrect because the y-values are doubled, not halved.
C
The conclusion is incorrect because the range is limited to the set of integers.
D
The conclusion is incorrect because the range is limited to the set of positive real numbers.
Explanation
For the exponential function f(x) = 2^x, increasing x by 1 doubles the output, and decreasing x by 1 halves it, so both statements describe the function’s changes correctly. But the range is limited to positive real numbers: 2^x is always greater than 0 and never reaches 0 or becomes negative. Thus the range limit is the issue described in choice D.
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