By solving a system of equations, we will see that the rational function is:
[tex]f(x) = \frac{12}{(x + 2)} -3[/tex]
Which rational function is graphed below?
First, we need to see the x-value of the vertical asymptote, here we can see that the vertical asymptote happens at x = -2, then the denominator will be something like:
d = (x - (-2)) = (x + 2).
Then our rational function will be something like:
[tex]f(x) = \frac{a}{(x + 2)} + c[/tex]
In the graph we can see two things, first:
f(0) = 3
f(1) = 1
Replacing that in our function, we get:
[tex]\frac{a}{(0 + 2)} + c = 3\\\\ \frac{a}{(1 + 2)} + c = 1[/tex]
This is a system of equations, that can be rewritten as:
a/2 + c = 3
a/3 + c = 1
Isolathing c in both equations, we get:
a/2 - 3 = -c = a/3 - 1
Then we have:
a/2 - 3 = a/3 - 1
Now we can solve this for a:
a/2 - a/3 = 3 - 1
a/6 = 2
a = 2*6 = 12
And the value of c is given by:
-c = a/3 - 1 = 12/3 - 1 = 4 - 1 = 3
c = -3
Then the rational function is:
[tex]f(x) = \frac{12}{(x + 2)} - 3[/tex]
If you want to learn more about rational functions, you can read:
https://brainly.com/question/1851758
