TRANSFORMATIONS OF FUNCTION WORKSHEET FOR 11TH GRADE

(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 = x^1/3 given in the following figure, draw

(i) y = −x^1/3

(ii) y = x^1/3 + 1 

(iii) y = x^1/3 - 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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