1. **Problem Statement:** We are given four linear functions defined on the domain $-4 \leq x \leq 6$: (a) $f(x) = 5x - 2$ (b) $f(x) = 5x + 2$ (c) $f(x) = -5x - 2$ (d) $f(x) = -5x + 2$ 2. **Formula and Rules:** A linear function has the form $f(x) = mx + b$ where $m$ is the slope and $b$ is the y-intercept. - The slope $m$ tells us how steep the line is and the direction it goes (positive slope means rising, negative means falling). - The y-intercept $b$ is the point where the line crosses the y-axis (when $x=0$). - The domain restriction $-4 \leq x \leq 6$ means we only plot points for $x$ values in this range. 3. **Intermediate Work and Explanation:** - For (a) $f(x) = 5x - 2$: - Slope $m=5$ (line rises steeply) - Y-intercept $b=-2$ - Calculate endpoints: - At $x=-4$, $f(-4) = 5(-4) - 2 = -20 - 2 = -22$ - At $x=6$, $f(6) = 5(6) - 2 = 30 - 2 = 28$ - For (b) $f(x) = 5x + 2$: - Slope $m=5$ - Y-intercept $b=2$ - Endpoints: - At $x=-4$, $f(-4) = 5(-4) + 2 = -20 + 2 = -18$ - At $x=6$, $f(6) = 5(6) + 2 = 30 + 2 = 32$ - For (c) $f(x) = -5x - 2$: - Slope $m=-5$ (line falls steeply) - Y-intercept $b=-2$ - Endpoints: - At $x=-4$, $f(-4) = -5(-4) - 2 = 20 - 2 = 18$ - At $x=6$, $f(6) = -5(6) - 2 = -30 - 2 = -32$ - For (d) $f(x) = -5x + 2$: - Slope $m=-5$ - Y-intercept $b=2$ - Endpoints: - At $x=-4$, $f(-4) = -5(-4) + 2 = 20 + 2 = 22$ - At $x=6$, $f(6) = -5(6) + 2 = -30 + 2 = -28$ 4. **Summary:** Each function is a straight line with slope and intercept as given. The domain limits the graph to $x$ values between $-4$ and $6$. Plotting the endpoints and connecting them with a straight line will give the graph of each function. **Final answers:** - (a) Line from $(-4, -22)$ to $(6, 28)$ - (b) Line from $(-4, -18)$ to $(6, 32)$ - (c) Line from $(-4, 18)$ to $(6, -32)$ - (d) Line from $(-4, 22)$ to $(6, -28)$