The function g(x) = 2^x. The function f(x) = 2^x + k and k < 0. Which of the following statements is true?​

The graph of f(x) is shifted k units above the graph of g(x). Therefore, the option C is the correct answer.

What is the function?

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are g(x) = 2ˣ and f(x) = 2ˣ+k

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Parent Function: g(x)=2x

Horizontal Shift: None

Vertical Shift: None

Reflection about the x-axis: None

Vertical Compression or Stretch: None

So, from graph of g(x) to the graph of f(x), it shifted k units up.

Therefore, the option C is the correct answer.

To learn more about the function visit:

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"Your question is incomplete, probably the complete question/missing part is:"

The function g(x) = 2ˣ. The f(x) = 2ˣ+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).

Answer:

Step-by-step explanation:

Please, when you see the words "the following statements," share those possible answer choices.  Thank you.

The function f(x) has the same graph as does g(x) EXCEPT that the graph has been translated down by |k| units.  

If k = -5 then the graph of f(x) is the same as that of g(x) except that it's been translated down 5 units.