RATIONAL FUNCTIONS & EXPRESSIONS

RATIONAL FUNCTIONS & EXPRESSIONS

Open Ended

 $Solve:\ \ \ \frac{x-1}{2x-4}+\frac{x+2}{3x}=1$  

Open Ended

 $Solve:\ \ \ \frac{4x}{x+4}+3=\frac{2}{x}$  

Open Ended

 $Find\ the\ solution\left(s\right):\ \ \frac{x^2-1}{x-1}=-2$  

Open Ended

 $f\left(x\right)=\frac{2x-6}{x^2-9}$  

For the given rational function find:
1. Domain
2. Range
3. X-intercept(s)
4. Y-intercept
5. Vertical Asymptote
6. Horizontal Asymptote
7. Removable Discontinuities
8. Sketch it.

Open Ended

List the transformations performed over the parent rational function f(x)=1/x to produce g(x)=-3f(x+1)-2

1.

2.

3.

4.

Open Ended

 $f\left(x\right)=\frac{x^2+2x}{x^2-2x-8}$  

1. Domain

2. Range

3. Vertical Asymptote(s)

4. Horizontal Asymptote

5. X and Y intercepts

6. Holes

7. Sketch and End Behavior

Fill in the Blank

 $Given\ \ f\left(x\right)=\frac{6x^2-5x+9}{3x-1}$  
Find:
1. Removable Discontinuities

2. Non removable Discontinuities

3. Oblique Asymptote

4. End Behavior

Open Ended

 $Find:\ \lim_{x\rightarrow3^-}=\ \ \ \ \ \ \ \ \ \ \ and\ \ \ \ \ \lim_{x\rightarrow3^+}=$   $\ \ \ \ \ \ \ \ \ \ if\ \ \ \ \ \ f\left(x\right)=\frac{4x-12}{x^2-9}$   



1. Left Side Behavior when approaching 3 from the left

2. Right Side Behavior when approaching 3 from the right