Question

Which of the following could be the graph of y = xn where n is even?

Answer 1

Answer:

3. The graph opening upwards

Step-by-step explanation:

We are given the function $y=x^{n}$, where n is even.

Now, we know that a polynomial function given by,

$y=a_{n}x^{n}+a_{n-1}x^{n-1} + .... + a_{1}x + a_{0}$.

Also, when the polynomial function has an even degree ( i.e. n = even ) with leading co-efficient positive ( i.e. $a_{0}$ > 0 ), its graph opens upwards.

As, we have that $y=x^{n}$ is also a polynomial function with degree ( n ) given to be even and the leading co-efficient is 1 > 0.

Hence, the graph of  $y=x^{n}$ will open upwards.

So, we get that the graph in figure 3 is the correct option.

Answer 2

The answer is C because is n is positive and even it will only open up.