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oksian1 [2.3K]
3 years ago
9

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:

Mathematics
2 answers:
GalinKa [24]3 years ago
8 0

<u>General Idea:</u>

Domain is the values of x which gives a defined output to the function, and Range is the values of y that we get by substituting domain values of x. For the function f(x) = a^x, where a > 0, the domain will be all real numbers and range will be all values greater than 0. That is the graph will be very close to x-axis but will never touch it.

<u>Applying the concept:</u>

From the attached table, we can notice that as x increases infinitely, the y-values are continually doubled for each single increase in x and as x decreases infinitely, the y-values are continually halved for each single decrease in x.

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

Option 1 is INCORRECT because Statement 1 is TRUE & CORRECT.

Option 2: "Statement 2 is incorrect because the y-values are doubled, not halved".

Option 2 is INCORRECT because Statement 2 is TRUE & CORRECT.

Option 3: "The conclusion is incorrect because the range is limited to the set of the integers"

Option 3 is INCORRECT because, the range will be always greater than 0, because irrespective of how many times y is halved for each single decrease in x, the y will still be a positive fraction and won't be a negative.

Option 4: "The conclusion is incorrect because the range is limited to the set of positive real numbers"

<em><u>Option 4 is CORRECT because y value will be positive irrespective of whatever x we substitute in the function.</u></em>

Inga [223]3 years ago
4 0

Answer:

Option 4 is the Correct answer!

Hope I helped! :}

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