The function g(x) = 2^x. the function f(x) = 2^x+k and k < 0. which of the following statements is true? a) the graph of f(x) is shifted k units to the left of the graph of g(x). b) the graph of f(x) is shifted k units to the right of the graph of g(x). c) the graph of f(x) is shifted k units above the graph of g(x). d) the graph of f(x) is shifted k units below the graph of g(x).

Option D)

Step-by-step explanation:

If the graph of the function  represents the transformations made to the graph of  then, by definition:

If  the graph moves vertically b units up

If the graph moves vertically b units down

If  the graph moves horizontally h units to the left

If the graph moves horizontally h units to the rigth

In this problem we have the function and our parent function is

therefore it is true that  and

Then "The graph of f(x) is shifted k units below the graph of g(x)".

The answer is Option D)

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Note:

If the function are:

Then and . This means that the function f(x) shifts k units to the right of the function g(x)

And the answer would be the option B)

B) The graph of f(x) is shifted k units to the right of the graph of g(x).

Step-by-step explanation:

We given the functions and where .

We know that horizontal depends on the value of x and are when

when graph is shifted to left; and

when graph is shifted to right.

Given the above functions, when k is considered positive then f(x) becomes .

Therefore, the graph of f(x) is shifted k units to the right of the graph of g(x).

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