Question: Use the graph to determine the following. a. the function's domain b. the function's range c. the x-intercepts, if any d. the y-intercept, if any e. the function value f left parenthesis negative 2 right parenthesis A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and vertical y-axis labeled from negative 10 to 10 in increments of 1. A curve falls from left to right from an open circle at left parenthesis negative 3, 8 right parenthesis to a closed circle at left parenthesis 0, negative 1 right parenthesis, passing through the points left parenthesis negative 2, 3 right parenthesis and left parenthesis negative 1, 0 right parenthesis .

1. **State the problem:** We are given a graph of a function with points and asked to find: a. the domain b. the range c. the x-intercepts d. the y-intercept e. the value of the function at $x=-2$ 2. **Analyze the graph:** - The curve starts at an open circle at $(-3,8)$ and ends at a closed circle at $(0,-1)$. - It passes through $(-2,3)$ and $(-1,0)$. 3. **Find the domain:** - The domain is the set of all $x$ values for which the function is defined. - Since the curve starts at $x=-3$ (open circle means $-3$ is not included) and ends at $x=0$ (closed circle means $0$ is included), the domain is: $$(-3, 0]$$ 4. **Find the range:** - The range is the set of all $y$ values the function takes. - The highest $y$ value is $8$ at $x=-3$ (open circle, so $8$ is not included). - The lowest $y$ value is $-1$ at $x=0$ (closed circle, so $-1$ is included). - The function passes through $3$ and $0$ as well. - So the range is: $$(-1, 8)$$ Note: Since the open circle at $8$ means $8$ is not included, and the closed circle at $-1$ means $-1$ is included, the range is actually: $$[-1, 8)$$ 5. **Find the x-intercepts:** - The x-intercepts are points where $y=0$. - The graph passes through $(-1,0)$, so the x-intercept is: $$-1$$ 6. **Find the y-intercept:** - The y-intercept is where $x=0$. - The graph has a closed circle at $(0,-1)$, so the y-intercept is: $$-1$$ 7. **Find $f(-2)$:** - From the graph, at $x=-2$, $y=3$. - So: $$f(-2) = 3$$