Rational Functions of the form $f\left(x\right)=\frac{ax+b}{cx+d}$
$y$-intercept
To find the $y$-intercept of a function, we substitute $x=$
Find the
coordinates of the $y$-intercept for each of the following functions.
If there is no $y$-intercept, enter "none".
$$f\left(x\right)=\frac{x+2}{x-1}$$
$$j\left(x\right)=\frac{-x+3}{x+3}$$
$$g\left(x\right)=\frac{2x-2}{x+2}$$
$$k\left(x\right)=\frac{-2x+4}{x-1}$$
$$h\left(x\right)=\frac{3x-1}{x+2}$$
$$l\left(x\right)=\frac{-3x+3}{x}$$
$f\left(x\right):$
$g\left(x\right):$
$h\left(x\right):$
$j\left(x\right):$
$k\left(x\right):$
$l\left(x\right):$
$x$-intercept
To find the $x$-intercept of a function, we let the function, for example $f\left(x\right)=$
Find the coordinates of the $x$-intercept for each of the functions above.
If there is no $x$-intercept, enter “none”.
$f\left(x\right):$
$g\left(x\right):$
$h\left(x\right):$
$j\left(x\right):$
$k\left(x\right):$
$l\left(x\right):$
Write down the equation of the vertical asymptote for each of the functions.
$$f\left(x\right)=\frac{x+2}{x-1}$$
$$j\left(x\right)=\frac{-x+3}{x+3}$$
$$g\left(x\right)=\frac{2x-2}{x+2}$$
$$k\left(x\right)=\frac{-2x+4}{x-1}$$
$$h\left(x\right)=\frac{3x-1}{x+2}$$
$$l\left(x\right)=\frac{-3x+3}{x}$$
$f\left(x\right):$
$g\left(x\right):$
$h\left(x\right):$
$j\left(x\right):$
$k\left(x\right):$
$l\left(x\right):$
Write down the equation of the horizontal asymptote for each of the functions.
$f\left(x\right):$
$g\left(x\right):$
$h\left(x\right):$
$j\left(x\right):$
$k\left(x\right):$
$l\left(x\right):$
Look at the equations of the functions and the equations of the vertical and horizontal asymptotes.
The equation of the vertical asymptote for the function $\displaystyle\frac{ax+b}{x+d}$ is $x=$
The equation of the horizontal asymptote for the function $\displaystyle\frac{ax+b}{x+d}$ is $y=$
Write down the equation of the vertical asymptote for each of the functions.
$$p\left(x\right)=\frac{x+3}{2x}$$
$$s\left(x\right)=\frac{2x+1}{3x}$$
$$q\left(x\right)=\frac{x+2}{2x-4}$$
$$t\left(x\right)=\frac{4x-3}{2x+2}$$
$$r\left(x\right)=\frac{-x-1}{3x+6}$$
$$w\left(x\right)=\frac{-4x+6}{3x+2}$$
$p\left(x\right):$
$q\left(x\right):$
$r\left(x\right):$
$s\left(x\right):$
$t\left(x\right):$
$w\left(x\right):$
Write down the equation of the horizontal asymptote for each of the functions.
$p\left(x\right):$
$q\left(x\right):$
$r\left(x\right):$
$s\left(x\right):$
$t\left(x\right):$
$w\left(x\right):$
Look at the equations of the functions and the equations of the vertical and horizontal asymptotes.
The equation of the vertical asymptote for the function $\displaystyle\frac{ax+b}{cx+d}$ is $x=$
The equation of the horizontal asymptote for the function $\displaystyle\frac{ax+b}{cx+d}$ is $y=$