1. The problem is to understand how to draw a function or graph "over the line," which typically means plotting a function on or above a certain line. 2. To do this, we first identify the line equation, for example, $y = mx + b$. 3. Then, we consider the function $y = f(x)$ that we want to draw over this line. 4. The condition for the function to be "over the line" is $f(x) \geq mx + b$ for all $x$ in the domain. 5. For example, if the line is $y = 2x + 1$, and the function is $y = x^2 + 3$, we check if $x^2 + 3 \geq 2x + 1$. 6. Simplify the inequality: $$x^2 + 3 \geq 2x + 1 \implies x^2 - 2x + 2 \geq 0.$$ 7. The quadratic $x^2 - 2x + 2$ has discriminant $\Delta = (-2)^2 - 4 \cdot 1 \cdot 2 = 4 - 8 = -4 < 0$, so it is always positive. 8. Therefore, $x^2 + 3$ is always above the line $y = 2x + 1$. 9. To draw the function over the line, plot both $y = 2x + 1$ and $y = x^2 + 3$ on the same axes, showing the function curve above the line.