geraldine is asked to explain the limits on the range of an exponential equation using the function…

geraldine is asked to explain the limits on the range of an exponential equation using the function (f(x)=2^{x}). 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 geraldines statements and her conclusion? statement 1 is incorrect because the (y - values) are increased by 2, not doubled. statement 2 is incorrect because the (y - values) are doubled, not halved. the conclusion is incorrect because the range is limited to the set of integers. the conclusion is incorrect because the range is limited to the set of positive real numbers.

geraldine is asked to explain the limits on the range of an exponential equation using the function (f(x)=2^{x}). 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 geraldines statements and her conclusion? statement 1 is incorrect because the (y - values) are increased by 2, not doubled. statement 2 is incorrect because the (y - values) are doubled, not halved. the conclusion is incorrect because the range is limited to the set of integers. the conclusion is incorrect because the range is limited to the set of positive real numbers.

Answer

Explanation:

Step1: Analyze the exponential function $f(x)=2^{x}$

For an exponential function of the form $y = a^{x}$ ($a>0,a\neq1$), when $a = 2$ and $x$ increases by 1, $y_{new}=2^{x + 1}=2\times2^{x}=2y_{old}$. So as $x$ increases infinitely, the $y -$values are continually doubled for each single increase in $x$, and statement 1 is correct.

Step2: Analyze the behavior when $x$ decreases

When $x$ decreases by 1, $y_{new}=2^{x-1}=\frac{2^{x}}{2}=\frac{y_{old}}{2}$. So as $x$ decreases infinitely, the $y -$values are continually halved for each single decrease in $x$, and statement 2 is correct.

Step3: Determine the range of $y = 2^{x}$

The exponential function $y = 2^{x}$ has a range of $(0,\infty)$ in the set of real - numbers. That is, the range is limited to the set of positive real numbers. So the conclusion that there are no limits within the set of real numbers on the range of this exponential function is incorrect.

Answer:

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