Question

Four curves i.e.
a) $y=x^3$
b) $y=x^7$
c) $y=x^2$ and
d) $y=x^6$
are depicted in the following graph.

Which polynomial is represented by Graph 4?

• A. $y=x^3$
• B. $y=x^7$
• C. $y=x^2$
• D. $y=x^6$

Answer 1

The correct option is A

$y=x^3$

As the value of the exponent ($n$) increases in the polynomial expression $x^n$, where n is an even number, then the curve i.e. the parabola gets closer to the y-axis.
Similarly, as the value of exponent ($n$) increases in the polynomial expression $x^n$ where n is an odd number, then the curve, which lies in the first and the third quadrants, gets closer to the y-axis.

The graph 4 is in the first and third quadrants. This means that the degree of the polynomial is odd.
Also, it is farther from the y-axis compared to graph 3. Thus, graph 4 represents $x^3$.