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

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Mathematics

Mattie Blankenship

16 July, 10:23

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

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Breanna · Answer 1

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?

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

Step-by-step explanation:

If the domain of a function given for "x" values for which the function is defined, then the range is the "y" values that the function takes. A simple exponential function as follows:

f (x) = 2x

has as its domain the real line and its range in the positive real numbers:

y > 0 : f (x)

it never takes a negative value nor reach 0

but it gets asymptotically closer as x goes to - ∞

Nor statement a: 1 is incorrect because the y-values are increased by 2, not doubled, or statement b: 2 is incorrect because the y-values are doubled, not halved, explains the accuracy of Geraldine's statements, neither does statement c: the conclusion is incorrect because the range is limited to the set of integers.