Answer:
B. The graph is symmetric about the origin
Step-by-step explanation:
We have the function [tex]y=a x^{n}[/tex], where a= 1 and n= odd.
'Leading Coefficient Test' states that 'when 'n' is odd and the leading coefficient is positive, then the graph falls to the left and rises to the right'.
As we have, [tex]y=x^{n}[/tex], where n is odd and leading coefficient a=1.
So, the graph of this function will fall to the left and rise to the right.
Then, option A is not correct.
Moreover, x= 0 ⇒ [tex]y=0^{n}[/tex] ⇒ y= 0.
So, this function passes though (0,0) i.e. origin.
Then, option C is not correct.
Also, 'x-intercept is the point when graph cuts the x-axis i.e. when y= 0'.
So, we have,
[tex]0=x^{n}[/tex] ⇒ x= 0.
Thus, the only x-intercept is the point (0,0).
Then, option D is not correct.
From the graph below, we see that, the graph of [tex]y=x^{n}[/tex] is symmetric about origin.
Hence, option B is correct.
