Question

The function g(x) = 2^x. The 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).

Answer 1

Using translation concepts, it is found that the correct option regarding function $f(x) = 2^x + k$ is:

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

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the parent and translated functions are given by, respectively:

$g(x) = 2^x$

$f(x) = 2^x + k, k < 0$

Since a negative number was added to g(x) to generate f(x), it is said that we have a shift down, hence option D is correct.

More can be learned about translation concepts at https://brainly.com/question/4521517