Question

Which statement describes the function y=ax^n when a=1 and n is odd?

Answer 1

ANSWER

B. The graph is symmetric about the origin

EXPLANATION.

The given function is

$y = a {x}^{n}$

When a=1,

$y = {x}^{n}$

Let,

$f(x)= {x}^{n}$

$f(-x)= {( - x)}^{n}$

Since n is odd,

$f(-x)=-{( x)}^{n}$

$\Rightarrow f(-x)=-f(x)$

This implies that, the function

$y={x}^{n}$

is symmetric with respect to origin.

The correct answer is B

Answer 2

Answer:

B. The graph is symmetric about the origin

Step-by-step explanation:

We have the function $y=a x^{n}$, 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, $y=x^{n}$, 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 ⇒ $y=0^{n}$ ⇒ 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,

$0=x^{n}$ ⇒ 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 $y=x^{n}$ is symmetric about origin.

Hence, option B is correct.