The function f(x) = (√2x² + 1)/(3x - 5) has a horizontal asymptote at y = 2/3 and a vertical asymptote at x = 5/3.
The function f(x) = (√2x² + 1)/(3x - 5) can have horizontal and vertical asymptotes. To find the horizontal asymptote, we need to consider the degrees of the numerator and denominator.
In this case, both the numerator and denominator have a degree of 2. Therefore, the ratio of the leading coefficients (2/3) gives us the equation of the horizontal asymptote, which is y = 2/3.
To find the vertical asymptote, we need to look for values of x that cause the denominator to equal zero. In this case, the denominator is 3x - 5. Setting this equal to zero gives us x = 5/3. Therefore, the equation of the vertical asymptote is x = 5/3.