Science:Math Exam Resources/Courses/MATH 180/December 2017/Question 11 (e)/Solution 1

Note that the domain of $P$ is given as $\{x\geq 0\}$.

Part (a) tells us that the graph of $P$ passes through $(0,0)$.

From part (b), we get the horizontal asymptote of $P$ as $y=0$. In other words, as $x$ goes to infinity, the graph approaches to $y=0$, i.e., $x$-axis.

From part (c) and (d), we see that $P$ is increasing on $[0,2)$ and decreasing on $(2,\infty )$, while it is concave down on $[0,4)$ and concave up on $(4,\infty )$.

Collecting the information, we can draw the graph of $P$ as follows.