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).

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luisejr77 luisejr77 · Answer 1 · 2019-04-13T22:09:40+02:00

Answer:

Option D)

Step-by-step explanation:

If the graph of the function [tex]f(x)=g(x+h) +b[/tex] represents the transformations made to the graph of [tex]y= g(x)[/tex] then, by definition:

If [tex]b> 0[/tex] the graph moves vertically b units up

If [tex]b <0[/tex] the graph moves vertically b units down

If [tex]h>0[/tex] the graph moves horizontally h units to the left

If [tex]h> 1[/tex] the graph moves horizontally h units to the rigth

In this problem we have the function [tex]f(x)=2^x+k[/tex] and our parent function is [tex]g(x) = 2^x[/tex]

therefore it is true that [tex]b =k<0[/tex] and [tex]h= 0[/tex]

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:

[tex]g(x) = 2^x\\\\f(x) = 2^{x+k}[/tex]

Then [tex]k = h[/tex] and [tex]h<0[/tex]. 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)

alinakincsem alinakincsem · Answer 2 · 2019-04-13T22:19:41+02:00

Answer:

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 [tex]g(x) = 2^x[/tex] and [tex]f(x)=2^{x+k}[/tex] where [tex]k <0[/tex].

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

[tex]g(x)=f(x+h)[/tex] when graph is shifted to left; and

[tex]g(x)=f(x-h)[/tex] when graph is shifted to right.

Given the above functions, when k is considered positive then f(x) becomes [tex]f(x)=2^{x+k}=g(x-k)[/tex].

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