Identify the oblique asymptote of f(x) = quantity x plus 4 over quantity 3 x squared plus 5 x minus 2.
Answers
Answer:
Step-by-step explanation: your question is incomplete . a complete question is ———> Identify the oblique asymptote of f(x) = quantity 3 x squared plus 2x minus 5 over quantity x minus 4.
y = 0
y = 3x − 10
y = 3x + 14
No oblique asymptote
Solve : you should first understand what is slant or oblique asymptote ?
A slant (oblique) asymptote occurs when the polynomial in the numerator is a higher degree than the polynomial in the denominator, To find the slant asymptote you must divide the numerator by the denominator ,
e.g., f(x) = (3x² + 2x - 5)/(x - 4)
= (3x² - 12x + 14x - 56 + 51)(/(x - 4)
= {3x(x - 4) + 14(x - 4) + 51}/(x -4)
= (3x + 14)(x - 4)/(x -4) + 51/(x - 4)
= 3x + 14 + 51/(x - 4)
At x → 4 ; f(x) → ± ∞
Hence, y = 3x + 14 is the oblique projectile