To sketch: The function by hand without plotting any points and then graph of the function .
The standard graph of the function is roughly drawn and shown below in Figure 1.
Then, draw the graph of by stretching the graph of vertically by a factor of 2. Thus, the graph of is shown below in Figure 2.
From Figure 2, it is observed that Figure 1 is stretchedvertically by a factor of 2.
Then, draw the graph of by reflecting the graph of about the origin. Thus, the graph of is shown below in Figure 3.
From Figure 3, it is observed that Figure 2 is reflected about the origin.
To draw the graph of , shift the graph by 3 units upward. Thus, the graph of is shown below in Figure 4.
Observe that Figure 4is obtainedfrom Figure 1 in such a way that it is stretched vertically by a factor of 2, reflect the graph about the origin and then shift 3 units upward.
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