The graph provided shows a quadratic function, and the problem is asking for two things:

1. $f(1)$: This is the value of the function when $x = 1$.
2. One value of $x$ where $f(x) = 1$.

Part (a) $f(1)$:

From the graph, we can see that when $x = 1$, the corresponding $y$-value is $-2$. Hence: $f(1) = -2$

Part (b) $f(x) = 1$:

We need to find one value of $x$ where $f(x) = 1$. From the graph, when $f(x) = 1$, one solution occurs at $x = 3$. Thus: $x = 3$

Would you like more details or further clarification?

Here are 5 related questions for further exploration:

1. What is the equation of this quadratic function?
2. Is there another value of $x$ where $f(x) = 1$?
3. Can you find the vertex of the quadratic function based on the graph?
4. How can you calculate the roots of the function from the graph?
5. What is the domain and range of the quadratic function based on this graph?

Tip: When analyzing a graph, always check the symmetry, as quadratic functions are symmetric around their vertex. This can help you find corresponding points easily!