Reciprocal (Rational) Functions

Multiple Choice

What is the correct "Parent function" for Rational (reciprocal) functions?

​Guided Notes:

​Guided Notes:

Multiple Choice

Identify the transformations & Asymptotes for $$f\left(x\right)=\frac{4}{x+1}-1$$  

• Move Right 1 and Up 0

  VA: x = 1

  HA: y = 0

• Move Left 1 and Up 4

  VA: x = -1

  HA: y = 4

• Move Right 4 and Down 1

  VA: x = 4

  HA: y = -1

• Move Left 1 and Down 1

  VA: x = -1

  HA: y = -1

Multiple Choice

Identify the transformations & Asymptotes for $$f\left(x\right)=\frac{3}{x-2}+2$$  

• Move Right 2 and Up 2

  VA: x = 2

  HA: y = 2

• Move Left 2 and Up 3

  VA: x = -2

  HA: y = 3

• Move Right 2 and Down 2

  VA: x = 2

  HA: y = -2

• Move Left 2 and Down 3

  VA: x = -2

  HA: y = -3

Multiple Choice

Identify the transformations & Asymptotes for $$f\left(x\right)=-\frac{1}{x+3}$$  

• Move Right 3 and Up 0

  VA: x = 3

  HA: y = 0

• Move Left 3 and Up 0

  VA: x = -3

  HA: y = 0

• Move Right 3 and Down 1

  VA: x = 3

  HA: y = -1

• Move Left 3 and Down 1

  VA: x = -3

  HA: y = -1

​Guided Notes:

Multiple Choice

Determine the graph for the following function:

$$f\left(x\right)=\frac{4}{x+1}-1$$  

Multiple Choice

Determine the graph for the following function:

$$f\left(x\right)=\frac{4}{x+2}$$  

Multiple Choice

Determine the graph for the following function:

$$f\left(x\right)=-\frac{1}{x+3}+1$$  

​Guided Notes:

​Guided Notes:

Multiple Choice

Identify the domain and range of the function:

$$f\left(x\right)=\frac{4}{x+1}+1$$  

• Domain: $$\left(-\infty,1\right)U\left(1,\infty\right)$$  

  Range:

  $$\left(-\infty,4\right)U\left(4,\infty\right)$$  

• Domain: $$\left(-\infty,4\right)U\left(4,\infty\right)$$  

  Range:

  $$\left(-\infty,-1\right)U\left(-1,\infty\right)$$  

• Domain: $$\left(-\infty,1\right)U\left(1,\infty\right)$$  

  Range:

  $$\left(-\infty,-1\right)U\left(-1,\infty\right)$$  

• Domain: $$\left(-\infty,-1\right)U\left(-1,\infty\right)$$  

  Range:

  $$\left(-\infty,1\right)U\left(1,\infty\right)$$  

Multiple Choice

Identify the domain and range of the function:

$$f\left(x\right)=\frac{3}{x-2}+2$$  

• Domain: $$\left(-\infty,-2\right)U\left(-2,\infty\right)$$  

  Range:

  $$\left(-\infty,2\right)U\left(2,\infty\right)$$  

• Domain: $$\left(-\infty,3\right)U\left(3,\infty\right)$$  

  Range:

  $$\left(-\infty,-2\right)U\left(-2,\infty\right)$$  

• Domain: $$\left(-\infty,2\right)U\left(2,\infty\right)$$  

  Range:

  $$\left(-\infty,2\right)U\left(2,\infty\right)$$  

• Domain: $$\left(-\infty,-3\right)U\left(-3,\infty\right)$$  

  Range:

  $$\left(-\infty,2\right)U\left(2,\infty\right)$$  

Multiple Choice

Identify the domain and range of the function:

$$f\left(x\right)=-\frac{1}{x+3}$$  

• Domain: $$\left(-\infty,-3\right)U\left(-3,\infty\right)$$  

  Range:

  $$\left(-\infty,0\right)U\left(0,\infty\right)$$  

• Domain: $$\left(-\infty,3\right)U\left(3,\infty\right)$$  

  Range:

  $$\left(-\infty,0\right)U\left(0,\infty\right)$$  

• Domain: $$\left(-\infty,0\right)U\left(0,\infty\right)$$  

  Range:

  $$\left(-\infty,3\right)U\left(3,\infty\right)$$  

• Domain: $$\left(-\infty,0\right)U\left(0,\infty\right)$$  

  Range:

  $$\left(-\infty,-3\right)U\left(-3,\infty\right)$$