Let's analyze the problem from the image:

You are given a plot of the function $f(x)$, and you need to:

1. Evaluate $f(1)$.
2. Solve $f(x) = 1$, i.e., find the value of $x$ when $f(x) = 1$.

Step 1: Evaluate $f(1)$

Looking at the graph, find the point where $x = 1$ and check the corresponding $y$-value (which is $f(1)$). It appears that at $x = 1$, the function reaches $f(1) = 4$.

So, $f(1) = 4$.

Step 2: Solve $f(x) = 1$

Now, find where the function equals 1, i.e., look for the value of $x$ such that $f(x) = 1$. By inspecting the graph, it looks like $f(x) = 1$ occurs at $x = 4$.

So, the solution to $f(x) = 1$ is $x = 4$.

Summary:

• $f(1) = 4$
• $f(x) = 1$ when $x = 4$

Would you like more details or explanations? Here are some questions to deepen your understanding:

1. What type of function could the graph represent (e.g., exponential, logarithmic)?
2. How would you solve $f(x) = 0$ using the graph?
3. What is the domain and range of this function based on the graph?
4. Can you describe the behavior of the function as $x \to \infty$?
5. How would you find $f'(1)$ if you were asked to compute the derivative?

Tip: When analyzing a graph, always check the behavior at key points like $x = 0$ and large values of $x$.