si elevas un numero entero al cuadrado y deaspues haces su raiz cuadrada, obtienes el mismo resulyado que si primero su raiz cuadrada y luego la elevas al cuadrado

solution: the steps to sketch the graph of rational function are (1) find x-intercept, (2) find y-intercepts, (3) find vertical asymptotes, (4) find horizontal asymptotes, (5) find coordinates of extreme points and (6) plot all points on coordinate plane and join them by a free hand curve.

explanation:

let the rational function is defined as .

the steps to sketch the graph of rational function are,

(1) find x-intercept: to find x-intercept set numerator equal to zero,   and find the real values of x.

(2) find y-intercept: to find y-intercept put x equal to zero,   and find the values of y.

(3) find vertical asymptote: to find vertical asymptotes set denominator equal to zero, and find the real values of x.

(4) find horizontal asymptotes: to find horizontal asymptotes notice the degree of numerator and denominator.

(i) if then the horizontal asymptote is .

(ii) if then the horizontal asymptote is a horizontal line , where a is the leading coefficient of p(x) and m is the leading coefficient of q(x).

(iii) if then the there is not horizontal asymptote exist but there is a slant asymptote with slope line , where a is the leading coefficient of p(x) and m is the leading coefficient of q(x).

(iv) if then the there is not horizontal asymptote exist.

(5) find the coordinates of extreme points: to find the coordinates of extreme points find the critical points by where r'(x) is the first derivative of r(x). then find second derivative if then it will give point of minima and if then it will give point of maxima. put these values of x in the original function to find the y-coordinate of extreme points.

(6) plot all points on coordinate plane and join them by a free hand curve.

therefore, the steps to sketch the graph of rational function are (1) find x-intercept, (2) find y-intercepts, (3) find vertical asymptotes, (4) find horizontal asymptotes, (5) find coordinates of extreme points and (6) plot all points on coordinate plane and join them by a free hand curve.