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Mathematics III Exploring rational functions

TECNOLGICO DE MONTERREYMath Department - VEM

Exploring rational functionsx

xf1

)( = and

Name_________________________________ID#. ____________ Date________

Objective: Using graphmatica analyze the transformations on the graphs ofx

xf1

)( =

and2

1)(

xxf = identifying domain, range, asymptotes and intercepts.

Previous Activity: Print this activityContents: Domain, range, asymptotes, rational functions and intercepts.Introduction: In this activity you will explore the different transformations of the graphs of

rational functionsRequired material: Activity 2.14 and laptop with graphmaticaEstimated time: 50 minutesDelivery form: You will hand in this activity individuallyInstructions: Read the instructions carefully, write out the problems, show complete procedure

and mark the final answer.Evaluation criteria: The activity will be graded by considering the number or correctly answers and

the procedure organization and neatnessHomework: Exercises 1-8 on page 350

I. Tell if the following statements are true or false.

1. ( ) The graph of 41

)( +=x

xP is a translation four units downward of the graphx

xP1

)( =

2. ( )The graph of 5

1)(

=

xxP is a translation five units to de right of the graph

xxP 1)( =

3. ( ) The graph of 2

1)(

xxP = + 5 shows a reflection over the X-axis and a vertical translation

5 units upwards of the graph2

1)(

xxP =

4. ( )The graph of 2)3(

1)(

=

xxP is a translation three units to de right of the graph

2

1)( xxP =

5. ( ) The vertical asymptote of the graph of 5

1)(

+

=

xxf is at 5=x

by: Lic. Mara de la Luz Sols


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6. ( ) The horizontal asymptote of the graph 61

)( +=x

xf is at 6=y

7. ( ) The graph of 2)3(

1)(

2

=

xxP is a translation three units to de right and down two

units, and then reflecting in the x-axis of the graph 21)( xxP =

8. ( ) The domain of 2

1)(

+

=

xxf is the set of real numbers except 2=x

9. ( ) The range of the graph of 3)2(

1)(

2+

=

xxf is the set of real numbers except 3=y

10. ( )The y-intercept of the graph of 12

1)( +

+

=

xxf is (0, )

II. Match the description of the translations of with its corresponding function.

1.( ) The function moves 4 units up and 3 units right.

2.( ) The function moves 2 units down, reflection over x-axis and moves 1

unit right.

3.( ) The function moves 3 units up and 4 units right.

4.( ) The function moves 1 unit down, reflection over x-axis and moves 2

units right.

5. ( ) The function moves 5 units up and moves 2 units right.

6.( ) The function moves 5 units up and moves 2 units left.

7.( ) The function moves 2 units up and moves 5 units left.

8. ( ) The function moves 4 units up and moves 3 units left.



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a) e)

b) f)

c) g)

d) h) 52

1)( +

=

xxf

III.Sketch the graph of the following functions showing the vertical and horizontal asymtotes as well

the x-intercept or y-intercepts, state the domain and range

1. 31

)( +=

x

xf

Domain Range

Vertical Asymptote X-intercept

Horizontal Asymptote Y. intercept

. 1

)3(

1)( +

=

x

xf

Domain Range



3. 32

1)(

+

=

xxf 4. 2

)4(

1)(

2+

=

xxf



4/5


Domain Range



Domain Range



5. 51

)(2+=

xxf

Domain Range



6.x

xf

=

4

1)(

Domain Range



7. 1)12(

1)(

2+

=

xxf 6. 2

32

1)(

+

=

xxf



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Domain Range



Domain Range




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