The quadratic function f(x) has these characteristics: The vertex is located at (1,8).
The range is -∞ < f(x) ≤8.
Which function could be the f(x)?

2x^2 + 4x + 6
2x^2 + x + 8
-2x^2 + 4x + 6
-2x^2 + x + 8

no oblique asymptote

step-by-step explanation:

to find the oblique asymptote of f(x)

here numerator has degree 1 and denomintor degree 2

degree of numerator < degree of denominator

hence there is no oblique asymptote

when the degree of the denominator > that of the numerator, we saw that the value in the denominator got so much bigger, so quickly,   giving us a horizontal asymptote of the x-axis. or we can write

f(x) = a polynomial of x + a proper fraction.

in this case only we have oblique asymptotes but not when numerator has less degree.