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. she concludes that there are no limits within the set of real numbers on the range of this exponential function. which best explains the accuracy of geraldine’s statements and her conclusion? 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.

As base of the exponential term 2 is greater than 1 so it will be exponential increasing graph as shown in attachment.

A.Statement 1 is incorrect because the y-values are increased by 2, not doubled.

Statement 1 was correct as value will be doubled with every increase in x.

We can check it this way

Like for

for (its double of 2)

for (its doubled of 4)

So statement 1 was correct

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B.Statement 2 is incorrect because the y-values are doubled, not halved.

This is also incorrect as statement 2 talks when x " decreases" then y will be halved

like you can check it this when

for

now when x is decreased from 3 to 2

then for (its half of 8)

so statement 2 was also correct

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C.The conclusion is incorrect because the range is limited to the set of integers.

This is also incorrect as we can have x as some non integer numbers like

for which is not integer

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D.The conclusion is incorrect because the range is limited to the set of positive real numbers.

This is correct as exponential terms will always be a positive number as you can see from graph in attachment, exponential curve will never cross x axis line or go below x axis, so it can never be negative. So range is all positrive real numbers

so choice (D) is the right answer

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step-by-step explanatio89