Algebra-2

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

 

1. Factorization

First, factor both the numerator and the denominator:

Numerator:

Denominator:

So the function can be written as .

 

 2. Asymptotes

Vertical Asymptotes:

Set the denominator equal to zero, , which gives and . So, there are vertical asymptotes at and .

 

Horizontal Asymptotes:

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

 

3. Intercepts

x-intercepts:

Set , we have , which implies . Solving for , we get <...