Algebra-2

To graph the function , we can analyze its key features as follows:

 

 1. Asymptotes

Vertical Asymptote:

We set the denominator equal to zero to find the vertical asymptote. For the function , we solve , which gives . So, there is a vertical asymptote at .

 

Horizontal Asymptote:

Since the degree of the polynomial in the numerator (degree ) is the same as the degree of the polynomial in the denominator (degree ), we can find the horizontal asymptote by taking the ratio of the coefficients of the highest degree terms.

The coefficient of in the numerator and the coefficient of in the denominator . So, the horizontal asymptote is .

 

 2. Intercepts

y-intercept:

To find the -intercept, we set in the function. So, . Thus, the -intercept is the point .

 

x-intercept:

To find the -intercept, we set . So, , which implies . Solving for , we get . So, the