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The problem asks you to describe how the graphs of \( f(x) \) and \( g(x) \) are related, and then write an equation for \( g(x) \).

### Step 1: Observe the Graphs

From the provided graphs:

- **Graph 1 (left)**: The function \( y = f(x) \) appears to be an increasing function that passes through the origin and grows as \( x \) increases. It has a curve that looks similar to a logarithmic or power function.
  
- **Graph 2 (right)**: The function \( y = g(x) \) appears to have the same shape as \( f(x) \) but is shifted upwards.

### Step 2: Identify the Relationship
It looks like the graph of \( g(x) \) is the same as \( f(x) \), but it is shifted upward by 2 units.

- The upward shift indicates that \( g(x) \) is a vertical translation of \( f(x) \) by 2 units.
  
### Step 3: Write the Equation
To express \( g(x) \) in terms of \( f(x) \), you add 2 to the function \( f(x) \) to account for the vertical shift. Therefore, the equation for \( g(x) \) is:

\[
g(x) = f(x) + 2
\]

### Summary:
- The graphs of \( f(x) \) and \( g(x) \) are identical in shape, but \( g(x) \) is shifted 2 units upward compared to \( f(x) \).
- The equation for \( g(x) \) is \( g(x) = f(x) + 2 \).

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Do you want further clarification on this? 

Here are 5 related questions you might consider:
1. What other transformations can be applied to a function besides vertical shifts?
2. How does a horizontal shift affect the equation of a function?
3. What is the effect of scaling a function vertically or horizontally?
4. Can you generalize the relationship between \( f(x) \) and \( g(x) \) to other functions with different transformations?
5. How would a reflection across the x-axis affect the graph of a function?

**Tip:** To visualize transformations easily, think of moving the entire graph up, down, left, or right depending on the type of transformation applied to the function.

Describe how the graphs f(x) and g(x) are related, then write an equation for g(x).

Learn how vertical shifts affect functions by comparing the graphs of f(x) and g(x). This problem explores transformations and the equation g(x) = f(x) + 2, suitable for high school students.

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