A function $f$ has a horizontal asymptote of $y = -4,$ a vertical asymptote of $x = 3,$ and an $x$-intercept at $(1,0).$ Part (a): Let $f$ be of the form $$f(x) = \frac{ax+b}{x+c}.$$Find an expression for $f(x).$ Part (b): Let $f$ be of the form $$f(x) = \frac{rx+s}{2x+t}.$$Find an expression for $f(x).$
A function $f$ has a horizontal asymptote of $y = -4,$ a vertical asymptote of $x = 3,$ and an $x$-intercept at $(1,0).$ Part (a): Let $f$ be of the form $$f(x) = \frac{ax+b}{x+c}.$$Find an expression for $f(x).$ Part (b): Let $f$ be of the form $$f(x) = \frac{rx+s}{2x+t}.$$Find an expression for $f(x).$
Part (a)
\(\large f(x)=\frac{8}{3-x}-4=\frac{8-12+4x}{3-x}\\ f(x) = \frac{ax+b}{x+c}\\ \large \color{blue}f(x)=\frac{-4x+4}{x-3}\)
a = -4; b = 4; c = -3
Part (b)
\(f(x)=\frac{rx+s}{2x+t}\\ \large \color{blue}f(x)=\frac{-8x+8}{2x-6}\)
r = -8; s = 8; t = -6
!
A function $f$ has a horizontal asymptote of $y = -4,$ a vertical asymptote of $x = 3,$ and an $x$-intercept at $(1,0).$ Part (a): Let $f$ be of the form $$f(x) = \frac{ax+b}{x+c}.$$Find an expression for $f(x).$ Part (b): Let $f$ be of the form $$f(x) = \frac{rx+s}{2x+t}.$$Find an expression for $f(x).$
Part (a)
\(\large f(x)=\frac{8}{3-x}-4=\frac{8-12+4x}{3-x}\\ f(x) = \frac{ax+b}{x+c}\\ \large \color{blue}f(x)=\frac{-4x+4}{x-3}\)
a = -4; b = 4; c = -3
Part (b)
\(f(x)=\frac{rx+s}{2x+t}\\ \large \color{blue}f(x)=\frac{-8x+8}{2x-6}\)
r = -8; s = 8; t = -6
!