Mathematics : Graphing rational expressions

Find the vertical asymptote of the function below:

y equals fraction numerator 3 over denominator x plus 1 end fraction minus 2


a. x=1

b. x=-1

c. x=2

d. x=-2



Find the vertical asymptote of the function below:

y equals fraction numerator 2 x plus 2 over denominator 3 x minus 1 end fraction


a.  x equals bevelled 1 third

b.  x equals minus bevelled 1 third

c.  x equals bevelled 2 over 3

d.  x equals minus bevelled 2 over 3



Find the horizontal asymptote of the function below:

y equals fraction numerator negative 2 over denominator x minus 4 end fraction minus 3


a. y=-2

b. y=4

c. y=3

d. y=-3



Find the horizontal asymptote of the function below:

y equals fraction numerator 2 x minus 8 over denominator x minus 5 end fraction


a. y=5

b. y=-5

c. y=2

d. y=-2



Which of the following graphs shows the function below?

f left parenthesis x right parenthesis space equals space fraction numerator x plus 2 over denominator x minus 1 end fraction space


a.  http://www.intervisualtechnology.us/data/1/15589/U6L4A.jpg

b.  http://www.intervisualtechnology.us/data/1/15590/U6L4B.jpg

c.  http://www.intervisualtechnology.us/data/1/15591/U6L4C.jpg

d.  http://www.intervisualtechnology.us/data/1/15592/U6L4D.jpg



Which of the following graphs shows the function below?

f left parenthesis x right parenthesis space equals space fraction numerator 2 x over denominator x minus 1 end fraction


a.  http://www.intervisualtechnology.us/data/1/15595/U6L4Q6A.jpg

b.  http://www.intervisualtechnology.us/data/1/15596/U6L4Q6B.jpg

c.  http://www.intervisualtechnology.us/data/1/15598/U6L4Q6D.jpg

d.  http://www.intervisualtechnology.us/data/1/15597/U6L4Q6C.jpg



Which of the following graphs shows the function below?

y equals fraction numerator 6 over denominator x plus 2 end fraction minus 6


a.  http://www.intervisualtechnology.us/data/1/15604/U6L4Q67A.jpg

b.  http://www.intervisualtechnology.us/data/1/15605/U6L4Q67B.jpg

c.  http://www.intervisualtechnology.us/data/1/15606/U6L4Q67C.jpg

d.  http://www.intervisualtechnology.us/data/1/15603/U6L4Q7D.jpg



Which of the following graphs shows the function below?

y equals fraction numerator 2 over denominator x minus 3 end fraction plus space 1


a.  http://www.intervisualtechnology.us/data/1/15607/U6L4Q8A.jpg

b.  http://www.intervisualtechnology.us/data/1/15608/U6L4Q8B.jpg

c.  http://www.intervisualtechnology.us/data/1/15609/U6L4Q8C.jpg

d.  http://www.intervisualtechnology.us/data/1/15610/U6L4Q8D.jpg



You paid $120 for a membership to a racquetball club. Court time is $4 per hour. Write a model that represents your average cost per hour of court time as a function of the number of hours played.


a.  f left parenthesis x right parenthesis space equals 4 over x plus 120

b.  f left parenthesis x right parenthesis space equals space fraction numerator 120 plus 4 x over denominator 4 end fraction

c.  f left parenthesis x right parenthesis space equals fraction numerator 120 plus 4 x over denominator x end fraction

d.  f left parenthesis x right parenthesis space equals x over 4 plus space 120



You paid $120 for a membership to a racquetball club. Court time is $4 per hour. Write a model that represents your average cost per hour of court time as a function of the number of hours played. What is the horizontal asymptote of this model and what does the asymptote represent?


a. y​ = 0; This asymptote represents the minimum amount paid per hour of court time.

b. y​ = 4; This asymptote represents the minimum amount paid per hour of court time.

c. y​ = 0; This asymptote represents the total number of hours of court time that needs to be paid for.

d. y​ = 4; This asymptote represents the total number of hours of court time that needs to be paid for.




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