Respuesta :
Answer:
Vertical Asymptote:
x=-5 , x=2
Horizontal Asymptote
y=3
Step-by-step explanation:
We are given function as
[tex]f(x)=\frac{3x^2+2x-1}{x^2+3x-10}[/tex]
Vertical asymptote:
For finding vertical asymptote , we can set denominator =0
and then we can solve for x
[tex]x^2+3x-10=0[/tex]
we can factor it
[tex](x+5)(x-2)=0[/tex]
[tex]x=-5,x=2[/tex]
Horizontal asymptote:
we can see that
degree of numerator =2
degree of denominator =2
So, degree of both numerator and denominator are same
So, for finding horizontal asymptote , we can find ratio of leading coefficient
Leading coefficient of numerator=3
leading coefficient of denominator =1
so, horizontal asymptote will be
[tex]y=\frac{3}{1}[/tex]
[tex]y=1[/tex]
Answer:
x = -5, x = 2 and y = 3
Step-by-step explanation:
The given function f(x) = (3x^2 - 2x - 1) /(x^2 + 3x - 10)
First let's find the horizontal asymptote.
Here the degree of the numerator and the denominator are the same. Which is 2.
Therefore, the horizontal asymptote = The leading coefficient of the numerator ÷ The leading coefficient of the denominator.
y = 3/1
y = 3
Now let's find the vertical asymptotes.
To find the vertical asymptotes set the denominator equal to zero and find the values of x.
x^2 + 3x - 10 = 0
(x - 2)(x + 5) = 0
x - 2 = 0 and x + 5 = 0
Solving the above, we get
x = 2 and x = -5
Therefore, the vertical asymptotes are at x =2 and x = -5
Answer: x = -5, x = 2 and y = 3.
Thank you.
