Question
What is the equation of the slant asymptote of the graph of the function f left parenthesis x right parenthesis equals Start Fraction 2 x squared minus 7 x minus 8 over x minus 4 End Fraction?
To find the equation of the slant asymptote, we need to divide the numerator by the denominator using long division.
2x^2 - 7x - 8
___________________
x - 4 | 2x^2 + 0x - 8
- (2x^2 - 8x)
_____________
8x - 8
- (8x - 32)
_____________
24
The result of the division is x + 8, which represents the slant asymptote.
Therefore, the equation of the slant asymptote is y = x + 8.