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 $g(x) = f(x) + 2$.

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.