Question

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).

Answer 1

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 $g(x) = 2^x$ and $f(x)=2^{x+k}$ where $k$.

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

$g(x)=f(x+h)$ when graph is shifted to left; and

$g(x)=f(x-h)$ when graph is shifted to right.

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

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

Answer 2

Answer:

Option D)

Step-by-step explanation:

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

If $b> 0$  the graph moves vertically b units up

If $b$ the graph moves vertically b units down

If $h>0$  the graph moves horizontally h units to the left

If $h> 1$ the graph moves horizontally h units to the rigth

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

therefore it is true that $b =k$  and $h= 0$

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:

$g(x) = 2^x\\\\f(x) = 2^{x+k}$

Then $k = h$ and $h$. 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)