Considering it's asymptotes and intercepts, the rational function is given by:
[tex]f(x) = 3\frac{x + 2}{(x + 1)^2}[/tex]
What are the asymptotes of a function f(x)?
- The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
- The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.
Looking at the graph, considering that the x-intercept is at x = -2, the vertical asymptote is at x = -1, and the horizontal asymptote is at y = 0(degree denominator > degree numerator), the rational function has the following format:
[tex]f(x) = a\frac{x + 2}{(x + 1)^2}[/tex]
The y-intercept is at y = 6, that is, when x = 0, f(x) = 6, hence:
[tex]a\frac{2}{1} = 6[/tex]
a = 3
Hence the function is:
[tex]f(x) = 3\frac{x + 2}{(x + 1)^2}[/tex]
More can be learned about rational functions at https://brainly.com/question/27880719
#SPJ1
