<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>
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