Question

Vertical asymptote as ( x rightarrow frac{-5}{4} ; y rightarrow pm infty )
vertical asymptote of ( f-1 )
= Move" a ental asymptote of ( f(x) )
( therefore )
as ( quad y rightarrow frac{3}{4} ; x rightarrow pm infty )
(i) ( x rightarrow-frac{5}{4} quad y=frac{a x+b}{4 x+c} )
be 15
( begin{aligned} c+4 x &=0 Rightarrow c-5 & Rightarrow c=5 end{aligned} quadleft[begin{array}{l}b cos ^{prime} t+a text { pest all it } c_{0}end{array}right. )
( y rightarrow frac{3}{4} quad x rightarrow pm infty )
( because quad y=frac{a x+b}{4 x+5}=frac{a+b / x}{4+5 / x} )
( operatorname{as} x rightarrow pm infty )
( y=frac{a}{4}=frac{3}{4} cdot 1, a=3 )
( y=frac{3 x+6}{4 x+5} quad ) At ( x=-frac{5}{4} quad begin{array}{l}3 x+6 eq 0 Rightarrow 12+quad-3 times 65end{array} )
( =frac{15}{4} )

# and Let fix) = ax + b for real a, b and c with a + 0. If the vertical asymptote of y = f(x) is x = 4x+c the vertical asymptote of y = f'(x) is x = - find the value(s) that b can take on. AW

Solution