Answer:
Correct answer: y = ( 3x² + 15x + 18) / (x² + 2x - 8)
Step-by-step explanation:
The function has vertical asymptotes at points where it is not defined.
In our case it is at x₁ = -4 and x₂ = 2
This means that the function in the denominator has a quadratic function whose roots are (x + 4) · (x - 2) = x² + 2x - 8
The function intercepts x axis at x₀₁ = -2 and x₀₂ = -3
This means that the function in the numerator has a quadratic function whose roots are (x + 2) · (x + 3) = x² + 5x + 6
The function currently looks like this:
y = (x² + 5x + 6) / (x² + 2x - 8)
Since the function has a horizontal asymptote y = 3, this means when x strive to + - infinite or x -> + - ∞ then it is
lim x -> + - ∞ (x² + 5x + 6) / (x² + 2x - 8) = 3
This means that the function in the numerator must has term 3x² which we will get when we multiply the currently function y = (x² + 5x + 6) / (x² + 2x - 8) by the number 3 and get :
y = 3 · (x² + 5x + 6) / (x² + 2x - 8) = (3x² + 15x + 18) / (x² + 2x - 8)
y = ( 3x² + 15x + 18) / (x² + 2x - 8)
God is with you!!!
