Question

(a) Draw the graph of the function P = 4x.
(b) From the graph, find the value of P, when
(i) x = 3
(ii) x = 4
(iii) x = 6

Answer 1

$$\begin{gathered} \left(\mathrm{a}\right)\mathrm{The}\mathrm{given}\mathrm{function}\mathrm{is}\mathit{}P=4x. \\ \mathrm{For}\mathrm{some}\mathrm{different}\mathrm{values}\mathrm{of}x,\mathrm{the}\mathrm{corresponding}\mathrm{values}\mathrm{of}P\mathrm{are}\mathrm{given}\mathrm{below}: \end{gathered}$$

x	0	1	2
P	0	4	8

$$\begin{gathered} \mathrm{On}\mathrm{a}\mathrm{graph}\mathrm{paper},\mathrm{plot}\mathrm{the}\mathrm{points}O\left(\mathit{0}\mathit{,}\mathit{0}\right)\mathit{,}\mathit{}A\left(\mathit{1}\mathit{,}\mathit{4}\right)\mathit{}\mathrm{and}B\left(\mathit{2}\mathit{,}\mathit{8}\right). \\ \mathrm{Join}\mathrm{them}\mathrm{successively}\mathrm{to}\mathrm{obtain}\mathrm{the}\mathrm{required}\mathrm{graph}. \end{gathered}$$



$$\begin{gathered} \left(\mathrm{b}\right) \\ \mathbf{Reading}\mathbf{}\mathbf{off}\mathbf{}\mathbf{from}\mathbf{}\mathbf{the}\mathbf{}\mathbf{graph} \\ \left(\mathrm{i}\right)\mathrm{On}\mathrm{the}\mathit{}x-\mathrm{axis},\mathrm{take}\mathrm{the}\mathrm{point}L\mathrm{at}x=3. \\ \mathrm{Draw}LR\mathit{\perp }x-\mathrm{axis},\mathrm{meeting}\mathrm{the}\mathrm{graph}\mathrm{at}R. \\ \mathrm{Clearly},RL=12\mathrm{units} \\ \therefore \mathit{}x=3\Rightarrow P=12 \\ \left(\mathrm{ii}\right)\mathrm{On}\mathrm{the}x-\mathrm{axis},\mathrm{take}\mathrm{the}\mathrm{point}M\mathrm{at}x=4. \\ \mathrm{Draw}MS\perp x-\mathrm{axis},\mathrm{meeting}\mathrm{the}\mathrm{graph}\mathrm{at}\mathit{}S. \\ \mathrm{Clearly}\mathit{,}\mathit{}SM=16\mathrm{units} \\ \therefore \mathit{}x=4\Rightarrow P=16 \\ \left(\mathrm{iii}\right)\mathrm{On}\mathrm{the}x-\mathrm{axis},\mathrm{take}\mathrm{the}\mathrm{point}N\mathrm{at}\mathit{}x=6. \\ \mathrm{Draw}NT\perp x-\mathrm{axis},\mathrm{meeting}\mathrm{the}\mathrm{graph}\mathrm{at}T. \\ \mathrm{Clearly},TN=24\mathrm{units} \\ \therefore x=6\Rightarrow P=24 \end{gathered}$$