Let's analyze the graph of the function $y = f(x)$ and solve each of the questions based on it.

1. Domain:

The domain refers to the set of all possible $x$-values for which the function is defined. Looking at the graph, the function appears to be defined from $x = -2$ to $x = 5$.

• Domain: $[-2, 5]$

2. Range:

The range is the set of all possible $y$-values the function can take. From the graph, the minimum value of $y$ is $y = -1$, and the maximum value is $y = 5$ at $x = 5$.

• Range: $[-1, 5]$

3. X-intercepts:

The x-intercept is where the graph crosses the x-axis (where $y = 0$). In this case, the graph does not intersect the x-axis, so there are no x-intercepts.

• X-intercepts: None

4. Y-intercept:

The y-intercept is the point where the graph crosses the y-axis (where $x = 0$). From the graph, when $x = 0$, $y = 1$.

• Y-intercept: $(0, 1)$

5. Missing Function Values:

We are asked to find $f(3)$. To do this, we look at the value of the function when $x = 3$. From the graph, $f(3) = 4$.

• $f(3)$: 4

Would you like any further clarifications or details on any part?

Follow-up questions:

1. What does the graph suggest about the behavior of the function as $x \to 5$?
2. Could the function be extrapolated beyond $x = 5$, and if so, what could happen?
3. How would you describe the concavity of the function based on the graph?
4. Can you derive the possible equation of the function given its shape and key points?
5. How does the domain or range change if the graph is shifted upwards by 2 units?

Tip:

Always check the graph carefully at the intercepts to ensure you're reading exact values, as slight errors can change the interpretation of the function!