Question 4.3: (a) Plot the graphs of y = x² and y=−x² on the same diagram.......

Essential Mathematics for Economics and Business [1390651]

(a) Plot the graphs of y = x² and y=−x² on the same diagram.
(b) Comment on the general properties of the graphs.

What is the effect on the graph of multiplying the right-hand side of each equation by (–1)?

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(a) Calculate a table of (x, y) points as in Table 4.1. Then graph these points as in Figure 4.4.
(b) From Figure 4.4, note the following. The graphs are symmetrical about the x-axis; that is, the graph of y = −x² is simply the graph of y = x² inverted. Therefore, multiplying the RHS of an equation y = f(x) by (−1) simply reflects its graph through the x-axis.

Table 4.1 Calculation of points for y = x² and y = –x²
x	f(x) = x²	f(x) = (−1)x²
-3	(−3)² =9	(−1)(−3)² =−9
-2	(−2)² =4	(−1)(−2)² =−4
-1	(−1)¹ =1	(−1)(−1)² =−1
0	(0)² =0	(−1)(0)² = 0
1	(1)² =1	(−1)(1)² =−1
2	(2)² =4	(−1)(2)² =−4
3	(3)² =9	(−1)(3)² =−9

4.4a

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