(1) For the curve y = x3 given in Figure, draw
(i) y = −x3
(ii) y = x3 + 1
(iii) y = x3 − 1
(iv) y = (x + 1)3 with the same scale. Solution
(2) For the curve y = x1/3 given in the following figure, draw
(i) y = −x1/3
(ii) y = x1/3 + 1
(iii) y = x1/3 - 1
(iv) y = (x + 1)1/3 Solution
(3) Graph the functions f(x) = x3 and g(x) = 3√x on the same coordinate plane. Find f ◦ g and graph it on the plane as well. Explain your results. Solution
(4) Write the steps to obtain the graph of the function y = 3(x − 1)2 + 5 from the graph y = x2 Solution
(5) From the curve y = sinx, graph the functions
(i) y = sin(−x)
(ii) y = −sin(−x)
(iii) y = sin (π/2+ x) which is cos x
(iv) y = sin (π/2− x) which is also cos x (refer trigonometry)
(6) From the curve y = x, draw
(i) y = −x
(ii) y = 2x
(iii) y = x + 1
(iv) y = (1/2)x + 1
(v) 2x + y + 3 = 0. Solution
(7) From the curve y = |x|, draw
(i) y = |x − 1| + 1
(ii) y = |x + 1| − 1
(iii) y = |x + 2| − 3 Solution
(8) From the curve y = sin x, draw y = sin|x| (Hint: sin(−x) = −sin x.) Solution
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