1. **State the problem:** Given the relation $R = \{(1, 2), (2, 4), (3, 9), (4, 16)\}$, determine if $R$ is a function by definition. 2. **Definition of a function:** A relation is a function if every element in the domain (first component) corresponds to exactly one element in the codomain (second component). 3. **Check the relation:** Each input value $1, 2, 3, 4$ maps to exactly one output value $2, 4, 9, 16$ respectively. 4. **Conclusion:** Since no input has more than one output, $R$ is a function. 1. **State the problem:** Using the vertical line test, confirm that the graph of $y = x^2$ represents a function. 2. **Vertical line test:** A graph represents a function if any vertical line intersects the graph at most once. 3. **Apply test to $y = x^2$:** For any vertical line $x = c$, the equation $y = c^2$ gives exactly one $y$ value. 4. **Conclusion:** Since vertical lines intersect the parabola only once, $y = x^2$ is a function. 1. **State the problem:** Draw the graph of $y = x^2$. 2. **Graph description:** The graph is a parabola opening upwards with vertex at the origin $(0,0)$. 3. **Plot points:** For example, $( -2, 4 ), ( -1, 1 ), (0, 0), (1, 1), (2, 4)$. 4. **Sketch:** Connect these points smoothly to form the parabola. **Final answers:** - Relation $R$ is a function. - The graph $y = x^2$ passes the vertical line test and represents a function. - The graph of $y = x^2$ is a parabola opening upwards centered at the origin.