1. **Problem Statement:** Define the graph of a function and draw the graph of the function $f(x) = |x - 3| + 5$. 2. **Definition:** The graph of a function is the set of all points $(x, y)$ in the coordinate plane such that $y = f(x)$. It visually represents how the output $y$ changes with the input $x$. 3. **Function Given:** $f(x) = |x - 3| + 5$. 4. **Important Rule:** The absolute value function $|x|$ outputs the distance of $x$ from zero, always non-negative. For $|x - 3|$, the graph is a V-shape with vertex at $x=3$. 5. **Vertex:** The vertex of $f(x)$ is at $x=3$, and $f(3) = |3 - 3| + 5 = 0 + 5 = 5$. So the vertex point is $(3, 5)$. 6. **Behavior:** For $x \\geq 3$, $f(x) = (x - 3) + 5 = x + 2$ (a line with slope 1). 7. For $x < 3$, $f(x) = -(x - 3) + 5 = -x + 3 + 5 = -x + 8$ (a line with slope -1). 8. **Summary:** The graph is a V-shaped graph with vertex at $(3, 5)$, opening upwards. 9. **Plotting Points:** - At $x=2$, $f(2) = |2-3| + 5 = 1 + 5 = 6$. - At $x=4$, $f(4) = |4-3| + 5 = 1 + 5 = 6$. 10. **Final Answer:** The graph of $f(x) = |x - 3| + 5$ is a V-shaped graph with vertex at $(3, 5)$, symmetric about the vertical line $x=3$, with arms rising linearly with slopes $1$ and $-1$ on either side.