ghe equations of the asymptotes. Che the graphs to determine each fometion’s dormain

Which transtormation is needed to graph the function ? Choose the correct anawer below.
A. The graph of should be shifted 3 unite to the left.
A. The graph of should be shifted 3 units to the right
C. The graph of should be shifted 3 units downward.
D. The graph of should be shifted 9 units upulard.

Ask by Mckenzie Barrett. in the United States

Mar 23,2025

Question

ghe equations of the asymptotes. Che the graphs to determine each fometion’s dormain

Which transtormation is needed to graph the function ? Choose the correct anawer below.
A. The graph of should be shifted 3 unite to the left.
A. The graph of should be shifted 3 units to the right
C. The graph of should be shifted 3 units downward.
D. The graph of should be shifted 9 units upulard.

Ask by Mckenzie Barrett. in the United States

Mar 23,2025

UpStudy AI · Accepted Answer

1. Start with the basic function:  
   $$
   f(x)=e^x
   $$

2. The function given is:  
   $$
   g(x)=e^{x+3}
   $$
   Recognize that $$g(x)$$ can be written as:
   $$
   g(x)=f(x+3)
   $$

3. For a function $$f(x+a)$$, the graph of $$f(x)$$ is shifted $$a$$ units to the left. Here, $$a=3$$.

4. Therefore, the graph of $$f(x)=e^x$$ should be shifted 3 units to the left.

The correct answer is:

A. The graph of $$ f(x)=e^{x} $$ should be shifted 3 units to the left.
To graph $$ g(x) = e^{x+3} $$, shift the graph of $$ f(x) = e^x $$ 3 units to the left.

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