The graphed rational function is:
[tex]f(x)= \frac{6}{x + 2}[/tex]
Which function is graphed below?
Here we can see that we have a rational function of the form:
[tex]f(x) = \frac{q(x)}{p(x)}[/tex]
Now we notice two things, as x increases, we have a horizontal asymptote that tends to zero.
Then q(x) is a constant, let's say:
q(x) = k
We also can see that we have a vertical asymptote at x = -2, then:
p(x) = (x + 2)
So the rational function is:
[tex]f(x) = \frac{K}{x + 2}[/tex]
Now, notice that when x = 0, the curve intercepts the y-axis at y = 3, then if we evaluate the function in x = 0 we must get:
[tex]f(0) = 3 = \frac{K}{0 + 2} = \frac{K}{ 2} \\\\3*2 = K = 6[/tex]
Then the rational function is:
[tex]f(x)= \frac{6}{x + 2}[/tex]
If you want to learn more about rational functions:
https://brainly.com/question/1851758
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