Final answer:
The slant asymptote of the function f(x) = (3x² + 2)/(x² - x - 7) is y = 3x + 8.
Step-by-step explanation:
To find the slant asymptote of the function f(x) = (3x² + 2)/(x² - x - 7), we need to divide the numerator by the denominator using polynomial long division. This will give us the quotient and remainder. The slant asymptote is then determined by the quotient. Let's proceed with the long division:
3x + 8
------------------
x² - x - 7 | 3x² + 0x + 2
- (3x² - 3x - 21)
3x + 23
So, the slant asymptote of the function f(x) = (3x² + 2)/(x² - x - 7) is y = 3x + 8.