why is the function y=x5−13 x≠0 non linear

The function y = x^5 - 13 is considered non-linear because it is a polynomial function with a degree greater than 1. In other words, when graphed, the resulting curve is not a straight line. Non-linear functions exhibit behavior that cannot be represented by a linear equation or graph, such as curves, loops, or other complex shapes.

x=0

I apologize for my previous response. The function y = x^5 - 13 is actually a nonlinear function due to the presence of the exponent 5. This exponent makes the function non-linear as it results in a curve when graphed. Additionally, x = 0 is not a valid input for this function as it leads to a division by zero, which is undefined. Thank you for pointing out the error in my explanation.