DL: W4 - Key Attributes of Rational Functions

Determine the attributes (choose 2): $f\left(x\right)=\frac{2}{x}+1$   

•  $V.A.\ @\ x=0,\ \ \ D:\ \left(-\infty,\ 0\right)\cup\left(0,\ \infty\right)$  

•  $V.A.\ @\ x=1,\ \ \ D:\ \left(-\infty,\ 1\right)\cup\left(1,\ \infty\right)$  

•  $H.A.\ @\ y=1,\ \ \ R:\ \left(-\infty,\ 1\right)\cup\left(1,\ \infty\right)$  

•  $H.A.\ @\ y=0,\ \ \ R:\ \left(-\infty,\ 0\right)\cup\left(0,\ \infty\right)$  

Determine the attributes (choose 2): $f\left(x\right)=\frac{-\ 2}{\frac{2}{3}x+1}$   

•  $V.A.\ @\ x=0,\ \ \ D:\ \left(-\infty,\ 0\right)\cup\left(0,\ \infty\right)$  

•  $V.A.\ @\ x=-\frac{3}{2},\ \ \ D:\ \left(-\infty,\ -\frac{3}{2}\right)\cup\left(-\frac{3}{2},\ \infty\right)$  

•  $H.A.\ @\ y=-\frac{3}{2},\ \ \ R:\ \left(-\infty,\ -\frac{3}{2}\right)\cup\left(-\frac{3}{2},\ \infty\right)$  

•  $H.A.\ @\ y=0,\ \ \ R:\ \left(-\infty,\ 0\right)\cup\left(0,\ \infty\right)$  

Determine the attributes (choose 2): $y=\frac{-\ 2}{x}-3$   

•  $V.A.\ @\ x=0,\ \ \ D:\ \left(-\infty,\ 0\right)\cup\left(0,\ \infty\right)$  

•  $V.A.\ @\ x=-3,\ \ \ D:\ \left(-\infty,\ -3\right)\cup\left(-3,\ \infty\right)$  

•  $H.A.\ @\ y=-2,\ \ \ R:\ \left(-\infty,\ -2\right)\cup\left(-2,\ \infty\right)$  

•  $H.A.\ @\ y=-3,\ \ \ R:\ \left(-\infty,\ -3\right)\cup\left(-3,\ \infty\right)$  

Determine the attributes (choose 2): $y=\frac{1}{5x-1}+2$   

•  $V.A.\ @\ x=\frac{1}{5},\ \ \ D:\ \left(-\infty,\ \frac{1}{5}\right)\cup\left(\frac{1}{5},\ \infty\right)$  

•  $V.A.\ @\ x=2,\ \ \ D:\ \left(-\infty,\ 2\right)\cup\left(2,\ \infty\right)$  

•  $H.A.\ @\ y=2,\ \ \ R:\ \left(-\infty,\ 2\right)\cup\left(2,\ \infty\right)$  

•  $H.A.\ @\ y=\frac{1}{5},\ \ \ R:\ \left(-\infty,\ \frac{1}{5}\right)\cup\left(\frac{1}{5},\ \infty\right)$  

Determine the attributes (choose 2): $f\left(x\right)=\frac{3}{x-1}$   

•  $V.A.\ @\ x=0,\ \ \ D:\ \left(-\infty,\ 0\right)\cup\left(0,\ \infty\right)$  

•  $V.A.\ @\ x=1,\ \ \ D:\ \left(-\infty,\ 1\right)\cup\left(1,\ \infty\right)$  

•  $H.A.\ @\ y=1,\ \ \ R:\ \left(-\infty,\ 1\right)\cup\left(1,\ \infty\right)$  

•  $H.A.\ @\ y=0,\ \ \ R:\ \left(-\infty,\ 0\right)\cup\left(0,\ \infty\right)$  

Determine the attributes (choose 2): $f\left(x\right)=\frac{5}{\frac{1}{3}x+2}-1$   

•  $V.A.\ @\ x=-6,\ \ \ D:\ \left(-\infty,\ -6\right)\cup\left(-6,\ \infty\right)$  

•  $V.A.\ @\ x=-\frac{3}{2},\ \ \ D:\ \left(-\infty,\ -\frac{3}{2}\right)\cup\left(-\frac{3}{2},\ \infty\right)$  

•  $H.A.\ @\ y=5,\ \ \ R:\ \left(-\infty,\ 5\right)\cup\left(5,\ \infty\right)$  

•  $H.A.\ @\ y=-1,\ \ \ R:\ \left(-\infty,\ -1\right)\cup\left(-1,\ \infty\right)$  

Determine the attributes (choose 2): $y=\frac{1}{x+2}$   

•  $V.A.\ @\ x=0,\ \ \ D:\ \left(-\infty,\ 0\right)\cup\left(0,\ \infty\right)$  

•  $V.A.\ @\ x=-2,\ \ \ D:\ \left(-\infty,\ -2\right)\cup\left(-2,\ \infty\right)$  

•  $H.A.\ @\ y=-2,\ \ \ R:\ \left(-\infty,\ -2\right)\cup\left(-2,\ \infty\right)$  

•  $H.A.\ @\ y=0,\ \ \ R:\ \left(-\infty,\ 0\right)\cup\left(0,\ \infty\right)$  

Determine the vertical asymptote & domain: $f\left(x\right)=\frac{\left(x-5\right)}{\left(x+2\right)}$   

•  $V.A.\ @\ x=5,\ \ \ D:\ \left(-\infty,\ 5\right)\cup\left(5,\ \infty\right)$  

•  $V.A.\ @\ x=-2,\ \ \ D:\ \left(-\infty,\ -2\right)\cup\left(-2,\ \infty\right)$  

•  $V.A.\ @\ x=2,\ \ \ D:\ \left(-\infty,\ 2\right)\cup\left(2,\ \infty\right)$  

•  $V.A.\ @\ x=-5,\ \ \ R:\ \left(-\infty,\ -5\right)\cup\left(-5,\ \infty\right)$  

Determine the vertical asymptote & domain: $y=\frac{\left(x+1\right)}{\left(x-3\right)}$   

•  $V.A.\ @\ x=1,\ \ \ D:\ \left(-\infty,\ 1\right)\cup\left(1,\ \infty\right)$  

•  $V.A.\ @\ x=-1,\ \ \ D:\ \left(-\infty,\ -1\right)\cup\left(-1,\ \infty\right)$  

•  $V.A.\ @\ x=3,\ \ \ D:\ \left(-\infty,\ 3\right)\cup\left(3,\ \infty\right)$  

•  $V.A.\ @\ x=-3,\ \ \ R:\ \left(-\infty,\ -3\right)\cup\left(-3,\ \infty\right)$  

Determine the vertical asymptote & domain: $f\left(x\right)=\frac{\left(x+4\right)}{\left(2x-5\right)}$   

•  $V.A.\ @\ x=\frac{5}{2},\ \ \ D:\ \left(-\infty,\ \frac{5}{2}\right)\cup\left(\frac{5}{2},\ \infty\right)$  

•  $V.A.\ @\ x=-4,\ \ \ D:\ \left(-\infty,\ -4\right)\cup\left(-4,\ \infty\right)$  

•  $V.A.\ @\ x=-\frac{5}{2},\ \ \ D:\ \left(-\infty,\ -\frac{5}{2}\right)\cup\left(-\frac{5}{2},\ \infty\right)$  

•  $V.A.\ @\ x=5,\ \ \ R:\ \left(-\infty,\ 5\right)\cup\left(5,\ \infty\right)$