Function Type Domain Range D35642

1. **Problem Statement:** We are given a graph consisting of two parts: a closed line segment from approximately $(-4, -2)$ to $(0, 2)$ and a separate closed ray starting at approximately $(1, -3)$ going down-right. We need to determine if the function represented is discrete, continuous, or neither, and then find its domain and range. 2. **Definitions:** - A **discrete function** consists of isolated points with no connecting lines. - A **continuous function** has an unbroken graph with no gaps or jumps. - A function can be **neither discrete nor continuous** if it has parts that are continuous and parts that are isolated or disconnected. 3. **Analyzing the graph:** - The closed line segment from $(-4, -2)$ to $(0, 2)$ is continuous because it is a connected line segment. - The separate closed ray starting at $(1, -3)$ going down-right is also continuous on its own but disconnected from the first segment. Since the graph consists of two disconnected continuous parts, the overall function is **neither discrete nor continuous** because it is not one continuous piece. 4. **Domain:** - The domain of the first segment is all $x$ values from $-4$ to $0$ inclusive. - The domain of the ray starts at $x=1$ and extends to the right indefinitely. Therefore, the domain is: $$ ext{Domain} = [-4, 0] \cup [1, \infty)$$ 5. **Range:** - The range of the first segment goes from $y=-2$ at $x=-4$ up to $y=2$ at $x=0$. - The ray starts at $y=-3$ at $x=1$ and goes down-right, so $y$ decreases without bound. Therefore, the range is: $$ ext{Range} = [-2, 2] \cup (-\infty, -3]$$ 6. **Summary:** - The function is neither discrete nor continuous. - Domain: $[-4, 0] \cup [1, \infty)$ - Range: $[-2, 2] \cup (-\infty, -3]$