reciprocal of a function

Question

explain what occurs to the x-intercepts of a function, when sketching its reciprocal and why.

Answer 1

The x-intercepts of a function y = f(x) are the real values of x for which f(x) = 0.  

 

1/f(x) would be undefined at these x-values.  

 

Examples:  f(x) = (x-1)² has x-intercept at x = 1, but y = 1/(x-1)²                        has a vertical asymptote when x = 1.

 

                     f(x) = sinx has x intercepts 0, ±π, ±2π, ..., but                                      y = 1/(sinx) = cscx has vertical asymptotes x = 0,

                     x = ±π, x = ±2π,...