1. **State the problem:** We need to graph the piecewise function $$f(x) = \begin{cases} -3x - 15 & \text{if } x < -5 \\ 3x + 15 & \text{if } x \geq -5 \end{cases}$$ and understand its behavior at the point where the pieces meet, $x = -5$. 2. **Evaluate the function at the boundary $x = -5$:** For $x < -5$, the function is $f(x) = -3x - 15$. At $x = -5$, this gives: $$f(-5) = -3(-5) - 15 = 15 - 15 = 0$$ For $x \geq -5$, the function is $f(x) = 3x + 15$. At $x = -5$, this gives: $$f(-5) = 3(-5) + 15 = -15 + 15 = 0$$ 3. **Interpret the boundary values:** - The left piece has an open circle at $(-5, 0)$ because it is defined for $x < -5$ (not including $-5$). - The right piece has a closed circle at $(-5, 0)$ because it is defined for $x \geq -5$ (including $-5$). 4. **Graph behavior:** - For $x < -5$, the function is a line with slope $-3$ and y-intercept $-15$, sloping downward to the left. - For $x \geq -5$, the function is a line with slope $3$ and y-intercept $15$, sloping upward to the right. 5. **Summary:** The graph consists of two rays meeting at $(-5, 0)$ with an open circle on the left ray and a closed circle on the right ray. This matches the description given. **Final answer:** The piecewise function is graphed with an open circle at $(-5, 0)$ on the left ray $y = -3x - 15$ for $x < -5$ and a closed circle at $(-5, 0)$ on the right ray $y = 3x + 15$ for $x \geq -5$.