Determine if the function y=x5−13 , x≠0 , is a linear or nonlinear function. Enter 1 if the function is linear. Enter 2 if the function is nonlinear.
The function y = x^5 - 13 is a nonlinear function.
To determine whether a function is linear or nonlinear, we need to check if it satisfies the properties of a linear function. A linear function must have a constant rate of change, meaning that for any two points (x1, y1) and (x2, y2) on the graph, the difference in y-coordinates over the difference in x-coordinates should always be the same.
In this case, if we take two points on the graph, let's say (1, -12) and (2, -3), we can calculate the rate of change:
Rate of change = (y2 - y1) / (x2 - x1)
Rate of change = (-3 - (-12)) / (2 - 1) = 9
However, if we take two other points on the graph, such as (-1, -14) and (0, -13), we calculate the rate of change:
Rate of change = (y2 - y1) / (x2 - x1)
Rate of change = (-13 - (-14)) / (0 - (-1)) = -1
Since the rate of change is not constant, the function y = x^5 - 13 is nonlinear. Thus, we would enter 2 to indicate that the function is nonlinear.