Problema Solution
Write an equation for a rational function with:
Vertical asymptotes at x = -6 and x = 1
x intercepts at x = 3 and x = -4
y intercept at 3
Answer provided by our tutors
In our case:
n(x) = (x-(-6)))(x - 1) = (x + 6)(x - 1)
t(x) = (x - 3)(x - (-4)) = (x - 3)(x + 4)
Now we can write:
f(x) = (x - 3)(x + 4)/((x + 6)(x - 1)) + b
We find b using the fact that y intercept is 3 that f(0) = 3:
(0 - 3)(0 + 4)/((0 + 6)(0 - 1)) + b = 3
(-12)/(-6) + b = 3
-2 + b = 3
b = 5
The rational function is:
f(x) = (x - 3)(x + 4)/((x + 6)(x - 1)) + 5
click here to see the graph of the function
