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Continue Shopping `        SIR WILL YOU PLEASE DRAW AND EXPLAIN THE GRAPH OF X POWER X when x gr8r than 1 it is easy but when x is less than 1 it is becoming a bit complicated please draw it and explain`
8 years ago

```							Dear student,
For positive x, it will start near 1, for x near zero, then will dip  down before increasing up to f(1) = 1, then it will increase more than  exponentially for x > 1.  For negative values of x, most  values of f(x) will be complex numbers, so you would only be able to  plot scattered points on a real number graph.  For example  (-1/2)^(-1/2) = 1/sqrt(-1/2) which is imaginary, but (-1/3)^(-1/3) is  1/cube_root(-1/3) which is a real number. Rational negative values of x  should produce either pure real or pure imaginary values of f(x).  Irrational negative values of x will produce f(x) being a complex  number.  All negative integer values of x will result in f(x)  real. As x becomes more negative, the values of f(x) will be  exponentially closer to zero, but jumping between positive and negative  values. Example (-2)^(-2) = (-1/2)^2 = 1/4, but (-3)^(-3) = (-1/3)^3 =  -1/27  If you could plot an additional imaginary axis (perpendicular  to the x and to the y axis, in 3-dimensions), f(x) would be seen  spiraling around the x-axis, approaching the x-axis but never quite  getting there, as x gets more negative. For values of x where f(x) is  real, this is where the spiral intersects the 'real' x-y plane.

```
8 years ago
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