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 geraldine’s statements and her conclusion?

Consider the exponential function

By definition, the domain of a function is the set of input argument values for which the function is real and defined.

Let we take then

then

then

If we chose larger values of x, we get larger function values.

For example, If we take

Thus if we choose smaller and smaller values of x. the f unction values will be smaller and smaller functions.

Thus the domain of the function is the set of all real numbers.

Thus the range is limited to the set of positive real numbers. That is,

If we choose larger values of x, we will get larger function values, as the function values will be larger powers of 2.

If we choose smaller and smaller x values, the function values will be smaller and smaller fractions.

here you hope this .

step-by-step explanation:

hypotenuse = √(15² + 8²)

=  √(225 +64)

=  √(289) = 17

sin(x) = cos(y) = 8/17

they are identical so long as you are doing the sine of one angle and the cosine of the only other angle that isn't the right angle.

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step-by-step explanation: