Question: Use the graph to determine a. the function’s domain; b. the function’s range; c. the x-intercepts, if any; d. the y-intercept, if there is one; e. the following function values. f(-4) f(1) a. What is the domain? (-\infty,\infty) (Type your answer in interval notation.) b. What is the range? [-4,\infty) (Type your answer in interval notation.) Graph: top-right. A blue piecewise line rises from the bottom-left with a left arrow, goes through the point (-4, -4), then continues horizontally right along y = -2 with a right arrow; the graph is in the top-right of the page.

1. **State the problem:** We are given a graph of a piecewise function and need to find: a. The domain b. The range c. The x-intercepts d. The y-intercept e. The values of the function at $x=-4$ and $x=1$ 2. **Domain:** The domain is the set of all possible $x$ values for which the function is defined. - The graph extends infinitely to the left (indicated by the left arrow) and infinitely to the right (right arrow). - Therefore, the domain is all real numbers. $$\text{Domain} = (-\infty, \infty)$$ 3. **Range:** The range is the set of all possible $y$ values the function takes. - The graph passes through $(-4, -4)$ and then continues horizontally at $y = -2$ to the right. - The lowest $y$ value is $-4$ and the function goes up to infinity (since the left part rises infinitely). $$\text{Range} = [-4, \infty)$$ 4. **X-intercepts:** Points where the graph crosses the $x$-axis ($y=0$). - From the description, the graph does not cross or touch the $x$-axis. $$\text{X-intercepts} = \varnothing$$ 5. **Y-intercept:** Point where the graph crosses the $y$-axis ($x=0$). - The horizontal part of the graph is at $y = -2$ for $x > -4$. - At $x=0$, the function value is $-2$. $$\text{Y-intercept} = (0, -2)$$ 6. **Function values:** - $f(-4)$ is the $y$ value at $x=-4$, which is $-4$. - $f(1)$ is the $y$ value at $x=1$, which lies on the horizontal line $y=-2$. $$f(-4) = -4$$ $$f(1) = -2$$ **Final answers:** - Domain: $(-\infty, \infty)$ - Range: $[-4, \infty)$ - X-intercepts: None - Y-intercept: $(0, -2)$ - $f(-4) = -4$ - $f(1) = -2$