Graphing Rational Functions

1. State the vertical asymptote of this function.

[math]f\left(x\right)=\frac{x}{x-3}+1[/math]

[math]x=-1[/math] [math]x=-3[/math] [math]x=1[/math] [math]x=3[/math]

2. State the horizontal aysmptote of this function.

[math]f\left(x\right)=\frac{x}{x-3}+1[/math]

[math]y=2[/math] [math]y=1[/math] [math]y=3[/math] [math]y=-3[/math]

3. State the vertical asymptotes of this function.

[math]f\left(x\right)=\frac{x}{\left(x-2\right)\left(x+3\right)}+2[/math]

[math]x=-1[/math] and [math]x=4[/math] [math]x=1[/math] and [math]x=-4[/math] [math]x=3[/math] and [math]x=-2[/math] [math]x=-3[/math] and [math]x=2[/math]

4. State the horizontal asymptote of this function.

[math]f\left(x\right)=\frac{x}{\left(x-2\right)\left(x+3\right)}+2[/math]

[math]y=2[/math] [math]y=3[/math] [math]y=-2[/math] [math]y=1[/math]

5. Create a function that matches the following information.

horizontal asymptote at [math]y=1[/math][br]vertical asymptote with the curve headed the opposite directions at [math]x=2[/math]

6. Create a function that matches the following information.

horizontal asymptote at [math]y=0[/math][br]vertical asymptote with the curve headed the same direction at [math]x=-4[/math]