11 TH MATHS EXERCISE 1.4

JK MATHS

11th Maths Solutions Chapter 1 Sets

                           Ex 1.4

Question 1.
For the curve y = x3 given in Figure, draw
(i) r = -x3
(ii) y = x3 + 1
(iii) y = x3 – 1
(iv) y = (x + 1)3 with the same scale.

Solution:

(i) It is the reflection on y axis

(ii) The graph of y = x3 + 1 is shifted upward to 1 unit.

(iii) The graph of y = x3 – 1 is shifted downward to 1 unit.

(iv) The graph of y = (x + 1)3 is shifted to the left for 1 unit

Question 2.

Question 3.

Graph the functions f(x) = x3 and g(x) = x−−√3 on the same coordinate plane. Find fog and graph it on the plane as well. Explain your results.

Solution:

Question 4.
Write the steps to obtain the graph of the function y = 3(x – 1)2 + 5 from the graph y = x2.
Solution:
Draw the graph of y = x2
To get y = (x – 1)2 we have to shift the curve 1 unit to the right.
Then we have to draw the curve y = 3(x – 1)2 and finally, we have to draw y = 3(x – 1)2 + 5

Question 5.
From the curve y = sin x, graph the functions
(i) y = sin(-x)
(ii) y = -sin(-x)
(iii) y = sin (π2 + x) which is cos x
(iv) y = sin (π2 – x) which is also cos x (refer trigonometry)
Solution:
First we have to draw the curve y = sin x

(i) y = sin (-x) = – sin x = f(x)