The graph given below shows graphical representation of the following polynomials.
a) y=x3 b) y=x7 c) y=x2 d) y=x6
Identify the correct relation between the graphs (1 to 4) and the polynomials (a to d).
A
(a)−1,(b)−4,(c)−3,(d)−2
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B
(a)−2,(b)−1,(c)−3,(d)−4
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C
(a)−1,(b)−2,(c)−3,(d)−4
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D
(a)−4,(b)−3,(c)−1,(d)−2
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Solution
The correct option is D(a)−4,(b)−3,(c)−1,(d)−2 Consider the polynomial xn, where n > 0.
i) When n is even, the graph will be in the first and second quadrants. Also, as the value of n increases, the graph comes closer to the y-axis. ii) When n is odd, the graph will be in the first and third quadrants. Also, as the value of n increases, the graph comes closer to the y-axis.
Thus, the correct relation is (a)−4,(b)−3,(c)−1,(d)−2