Question

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

Answer 1

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

Answer 2

3. The graph opening upwards

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.