In the image, you are asked to use the graph to determine several properties of the function:

1. Function's Domain: The domain represents all possible values of $x$ for which the function is defined. From the graph (a parabola), it seems like the function is defined for all real values of $x$, meaning the domain is:

   $(-\infty, \infty)$

2. Function's Range: The range represents all possible values of $y$. The graph of the parabola has its vertex at the point $(0, -5)$ and opens upwards. Therefore, the smallest value of $y$ is $-5$, and it increases without bound. The range is:

   $[-5, \infty)$

3. X-Intercepts: X-intercepts are points where the graph crosses the $x$-axis (where $y = 0$). From the graph, the parabola appears to cross the $x$-axis at approximately $x = -3$ and $x = 3$. Therefore, the x-intercepts are:

   $x = -3, 3$

4. Y-Intercept: The y-intercept is where the graph crosses the $y$-axis (where $x = 0$). From the graph, the parabola crosses the $y$-axis at $y = -5$. Therefore, the y-intercept is:

   $y = -5$

5. Missing Function Values: You are asked to find $f(-2)$ and $f(2)$. From the graph:

   • At $x = -2$, the graph shows that $f(-2) = -1$.
   • At $x = 2$, the graph also shows that $f(2) = -1$.

To summarize:

• Domain: $(- \infty, \infty)$
• Range: $[-5, \infty)$
• X-Intercepts: $x = -3, 3$
• Y-Intercept: $y = -5$
• $f(-2) = -1$
• $f(2) = -1$

Let me know if you'd like more details or have questions!

Here are five additional related questions for practice:

1. What is the vertex form of the parabola shown?
2. How do you calculate the axis of symmetry of the parabola?
3. How would the graph change if the parabola opened downward instead of upward?
4. How do you find the focus and directrix of a parabola given its equation?
5. What does the discriminant of the quadratic function tell you about its x-intercepts?

Tip: Always look at the vertex of the parabola first to understand its direction and lowest/highest point when determining the range.