the Reciprocal Function (basic Rational Transformations)

​Now recall the transformation rules you learned during the prior units this semester!

• Vertical dilation by a factor of 2

• Horizontal translation right 3

• Vertical translation up 4

Multiple Choice

Given

$$y=\frac{2}{x-5}+3$$   Determine the Horizontal Asymptote

• $$y=2$$  

• $$y=0$$  

• $$y=3$$  

• $$y=5$$  

Fill in the Blank

Given

$$y=\frac{3}{x+7}+6$$  
Identify the horizonal asymptote

Fill in the Blank

Given

$$y=\frac{3}{x+7}+6$$  
Identify the vertical asymptote

Multiple Choice

What are the asymptotes?

• x=-3, y=1

• x=3, y =1

• x=-3, y =-1

• x=3 y=-1

Multiple Choice

Given

$$y=\frac{3}{\left(x-4\right)^2}-5$$  Determine the Vertical and Horizontal Asymptotes

• $$x=3\$$  and  $$y=5$$  

• $$x=4$$  and  $$y=-5$$  

• $$x=-4$$  and  $$y=5$$  

• $$x=-4$$  and  $$y=-5$$  

Multiple Choice

How is this function transformed from the parent function ?

$$y=\frac{1}{x}$$  

• Translated Right 5 and Up 1

• Translated Right 5 and Down 1

• Translated Left 5 and Up 1

• Translated Left 5 and Down 1

Multiple Choice

Describe the transformations from the parent function

$$y=\frac{1}{x}$$  

• Right 5  and  Up 7

• Left 7  and  Up 5

• Reflect over the x-axis  and  Up 7

• Left 5  and  Up 7

Multiple Choice

What is the equation of the graphed Rational transformation?

• $$y=\frac{1}{x-3}+5$$

• $$y=\frac{1}{x+3}-5$$

• $$y=\frac{1}{x-3}-5$$

• $$y=\frac{1}{x+3}+5$$

Multiple Choice

What are the values of a, h, and k?

$$y=\frac{1}{x+3}-2$$

• a = 1

  h = 3

  k= -2

• a = 1

  h = -3

  k = -2

• a = 1

  h = 3

  k = 2

• a = 1

  h = -3

  k = 2

Multiple Choice

Which are possible values of a, h, and k?

• a = 1

  h = -3

  k = 5

• a = 1

  h = 5

  k = -3

• a = -1

  h = -3

  k = 5

• a = -1

  h = 5

  k = -3

Multiple Choice

Which is not true?

• The graph is a reflection of the parent funtion $$y=\frac{1}{x}$$

• An equation for the function is $$y=\frac{-1}{x-1}$$

• There is a vertical asymptote at

  $$x=-1$$

• There is a horizontal asymptote at $$y=0$$

Multiple Choice

Given $$y=\frac{2}{x+1}-3$$ . Which is NOT a transformation from the parent funtion?

• The graph is reflected vertically

• The graph is shifted left 1

• The graph is shifted down 3

• The graph is stretched vertically

Multiple Choice

A rational function is shifted to the right 2 units and shifted up 4 units. Which is a possible equation?

• $$y=\frac{1}{x+4}+2$$

• $$y=\frac{1}{x-4}+2$$

• $$y=\frac{1}{x+2}+4$$

• $$y=\frac{1}{x-2}+4$$

Multiple Choice

Which is NOT true of the function below?

$$y=-\frac{2}{x+3}-1$$

• There is a vertical asymptote at $$x=3$$

• a = -2

  h = -3

  k = -1

• The range is $$\left(-\infty,\ -1\right)\cup\ \left(-1,\ \infty\right)$$

Multiple Choice

Which is the graph of $$y=-\frac{1}{x-2}$$ ?

Multiple Choice

Which equation matches the graph?

• $$y=\frac{1}{x+3}-1$$

• $$y=\frac{1}{x-3}-1$$

• $$y=-\frac{1}{x+3}-1$$

• $$y=-\frac{1}{x-3}-1$$

Multiple Choice

What is the parent function of a rational function?

• Y=X²
• Y=X
• 1 / X
• Y=X / 1

Multiple Choice

Which of the following is undefined?

• $$0$$

• $$\frac{0}{4}$$

• $$0$$

• $$\frac{6}{0}$$

Multiple Choice

Referring to f(x)=  $$\frac{1}{x}$$  how does f(x) =  $$\frac{1}{x+3}$$  translate?. 

• Shifts right 3

• Shifts up three

• Shifts left three

• Shifts down three

Multiple Choice

Referring to f(x)=  $$\frac{1}{x}$$  how does f(x) =  $$\frac{1}{x}+3$$  translate?

• Shifts right 3 units.

• Shifts up 3 units.

• Shifts left 3 units.

• Shifts down 3 units.

Multiple Choice

Referring to f(x) =  $$\frac{1}{x}$$  how does f(x) =   $$\frac{1}{x-4}+1$$ Translate. 

• Shifts left 4 units and up 1 unit.

• Shifts left 4 units and down 1 unit.
  

• Shifts right 4 units and up 1 unit.
  

• Shifts right 4 units and down 1 unit.

Multiple Choice

Referring to f(x) =  $$\frac{1}{x}$$  how does f(x) =  $$\frac{1}{x+2}-5$$  translate?

• Shifts left 2 units and up 5 units.

• Shifts right 2 units and up 5 units.
  

• Shifts right 2 units and down 5 units.

• Shifts left 2 units and down 5 units.

Multiple Choice

Referring to f(x) =  $$\frac{1}{x}$$  which function shifts right 10 units and down 4 units?

• F(x) =  $$\frac{1}{x-10}-4$$  

• F(x) =  $$\frac{1}{x+10}+4$$  

• F(x) =  $$\frac{1}{x-4}+10$$  

• F(x) =  $$\frac{1}{x+4}-10$$  

Multiple Choice

Referring to f(x) =  $$\frac{1}{x}$$  which function shifts down 6 units?

• F(x) = $$\frac{1}{x-6}$$  

• F(x) = $$\frac{1}{x}-6$$  

• F(x) = $$\frac{1}{x+6}$$  

• F(x) = $$\frac{1}{x}+6$$  

Multiple Choice

Identify the horizontal and the vertical asymptotes of the function shown in the graph.

• horizontal asymptote: y = -3; vertical asymptote: x = -4
• horizontal asymptote: x = 3; vertical asymptote: y = -4
• horizontal asymptote: y = -3; vertical asymptote: x = 4
• horizontal asymptote: x = -3; vertical asymptote: y = 4