Write an equation of the graph in its final position.
The graph of is translated 5 units to the left and then 2 units upward.
Which of the following is the equation of the graph?
A.
C.
D.

Ask by Guzman Zimmerman. in the United States

Jan 24,2025

Question

Write an equation of the graph in its final position.
The graph of is translated 5 units to the left and then 2 units upward.
Which of the following is the equation of the graph?
A.
C.
D.

Ask by Guzman Zimmerman. in the United States

Jan 24,2025

UpStudy AI · Accepted Answer

To find the equation of the graph after the specified translations, we need to follow these steps:

1. **Translation 5 units to the left**: When a graph is translated to the left, we replace $$ x $$ with $$ x + h $$, where $$ h $$ is the number of units translated. In this case, $$ h = 5 $$. Therefore, the equation becomes:
   $$
   y = 6^{x + 5}
   $$

2. **Translation 2 units upward**: When a graph is translated upward, we add the number of units to the entire function. Thus, we add 2 to the equation:
   $$
   y = 6^{x + 5} + 2
   $$

Now, let's summarize the transformations:
- Start with $$ y = 6^{x} $$
- After translating 5 units to the left: $$ y = 6^{x + 5} $$
- After translating 2 units upward: $$ y = 6^{x + 5} + 2 $$

Now, let's compare this with the options provided:
- A. $$ y = 6^{x + 5} - 2 $$
- C. $$ y = 6^{x - 5} + 2 $$
- D. $$ y = 6^{x - 5} - 2 $$

None of the options match $$ y = 6^{x + 5} + 2 $$. However, it seems there might be a misunderstanding in the options provided.

The correct final equation after the transformations is:
$$
y = 6^{x + 5} + 2
$$

Since this is not listed among the options, it appears there may be an error in the options provided. Please double-check the options or the problem statement.
The correct equation after translating $$ y = 6^{x} $$ 5 units to the left and 2 units upward is $$ y = 6^{x + 5} + 2 $$. None of the provided options match this equation.

Write an equation of the graph in its final position.
The graph of is translated 5 units to the left and then 2 units upward.
Which of the following is the equation of the graph?
A.
C.
D.

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Write an equation of the graph in its final position. The graph of is translated 5 units to the left and then 2 units upward. Which of the following is the equation of the graph? A. C. D.

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Write an equation of the graph in its final position.
The graph of is translated 5 units to the left and then 2 units upward.
Which of the following is the equation of the graph?
A.
C.
D.