Let's analyze the graph in the image and answer the questions accordingly.

1. Domain Interval:

The domain of a function is the set of all possible input values (x-values). Based on the graph:

• The function exists from $x = -4$ to $x = 4$.

Thus, the domain interval is: $\text{Domain Interval} = [-4, 4]$

2. Range Interval:

The range of a function is the set of all possible output values (y-values). From the graph:

• The minimum value of $y$ appears to be $y = -2$.
• The maximum value of $y$ appears to be $y = 3$.

So, the range interval is: $\text{Range Interval} = [-2, 3]$

3. Domain SB (Set Builder notation):

The domain in set-builder notation specifies the set of x-values. Based on the domain interval: $\text{Domain SB} = \{ x \mid -4 \leq x \leq 4 \}$

4. Range SB (Set Builder notation):

The range in set-builder notation specifies the set of y-values. Based on the range interval: $\text{Range SB} = \{ y \mid -2 \leq y \leq 3 \}$

5. Find $f(0)$:

To find $f(0)$, locate the y-value corresponding to $x = 0$ on the graph:

• From the graph, when $x = 0$, $y = 2$.

So: $f(0) = 2$

6. Find $f(-2)$:

To find $f(-2)$, locate the y-value corresponding to $x = -2$ on the graph:

• From the graph, when $x = -2$, $y = 1$.

So: $f(-2) = 1$

Would you like further details or explanations on any of these solutions?

Related Questions:

1. What would be the domain and range if the function was shifted 2 units up?
2. How would the graph change if reflected across the y-axis?
3. What is the significance of a function being continuous over its domain?
4. How do we determine the maximum and minimum values of a function from its graph?
5. What is the importance of understanding the domain and range in real-world applications?

Tip:

Always double-check the endpoints of a graph when determining the domain and range, especially if the function includes open or closed intervals.