Answer:
True
Step-by-step explanation:
Given that a function is
[tex]f(x)=\frac{x^2-4x+1}{2x-3}[/tex]
We are to find the slant asymptote if any for this function
Since numerator is of degree 2 and denominator 1, let us divide and then check
Doing long division we find
[tex]f(x)=\frac{1}{2} [x-\frac{5}{2} ]-\frac{11}{4(2x-3)}[/tex]
Thus we find the asymptote y= the quotient obtained i.e
[tex]\frac{1}{2} [x-\frac{5}{2} ]\\=\frac{x}{2} -\frac{5}{4}[/tex]
Hence asymptote is
[tex]y=1/2x-5/4[/tex]
Statement given is true.
