Question

Explain what happens to the graph of y = xn, where n is an even positive integer, as n increases. Describe changes for x between – 1 and 1 and for x greater than 1 or less than – 1. Explain why these changes happen.

Answer 1

If you typed the equation correctly, n increasing causes the line y=x to become closer to being a vertical line by changing the slope.

Answer 2

Explanation:

Given is an exponential equation as

`y=x^n`

where n is an even positive integer.

Because n is even positive we find that y(-x) = y(x)

Or the curve is symmetrical about x=0

When x lies between -1 and 1, y will be a decreasing function in (-1,0) attains minimum at origin and increases in the interval (0,1)

When n increases the spread becomes less.

This is because when symmetrical about y axis at 0, this attains minimum.

Whenever x >1, the curve continuously increases and for x<-1 the curve continuously decreases.