Question

The graph given below shows graphical representation of the following polynomials.

a) $y=x^3$
b) $y=x^7$
c) $y=x^2$
d) $y=x^6$


Identify the correct relation between the graphs $\left(1\text{to}4\right)$ and the polynomials $\left(a\text{to}d\right)$.

• A. $\left(a\right)-1,\left(b\right)-2,\left(c\right)-3,\left(d\right)-4$
• B. $\left(a\right)-4,\left(b\right)-3,\left(c\right)-1,\left(d\right)-2$
• C. $\left(a\right)-2,\left(b\right)-1,\left(c\right)-3,\left(d\right)-4$
• D. $\left(a\right)-1,\left(b\right)-4,\left(c\right)-3,\left(d\right)-2$

Answer 1

The correct option is B $\left(a\right)-4,\left(b\right)-3,\left(c\right)-1,\left(d\right)-2$

Consider the polynomial $x^n$, 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 $\left(a\right)-4,\left(b\right)-3,\left(c\right)-1,\left(d\right)-2$