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Mathematics LibreTexts

2.1E: Exercises

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Practice Makes Perfect

Represent Relations as Mapping Diagrams and Tables

For each of the following relations, create a mapping diagram and table.

  1. R={(17,3),(4,2),(2,0),(6,10),(7,8)}
  2. R={(0,3),(0,5),(0,7),(3,22),(5,16),(7,3),(7,11)}
  3. R={(5,1),(4,0),(3,1),(2,2)}
  4. R={(3,0),(2,3),(2,4),(1,5)}
Answer
Mapping diagram Table
exercises_dr_map_1.JPG xy171020426378
  1. Mapping diagram Table
    exercises_dr_map_2.JPG xy05030732251671173
  1. Mapping diagram Table
    exercises_dr_map_3.JPG xy51403122
  1. Mapping diagram Table
    exercises_dr_map_4.JPG xy30232415
Determine the domain of a relation

For each relation below, determine the domain.

  1. R={(17,3),(4,2),(2,0),(6,10),(7,8)}
  2. R={(0,3),(0,5),(0,7),(3,22),(5,16),(7,3),(7,11)}
  3. R={(5,1),(4,0),(3,1),(2,2)}
  4. R={(3,0),(2,3),(2,4),(1,5)}
Answer
  1. {17,2,4,6,7}
  2. {0,3,5,7}
  3. {5,4,3,2}
  4. {3,2,1}
Determine the range of a relation

For each relation below, determine the range.

  1. R={(17,3),(4,2),(2,0),(6,10),(7,8)}
  2. R={(0,3),(0,5),(0,7),(3,22),(5,16),(7,3),(7,11)}
  3. R={(5,1),(4,0),(3,1),(2,2)}
  4. R={(3,0),(2,3),(2,4),(1,5)}
Answer
  1. {10,0,2,3,8}
  2. {11,5,3,7,16,22}
  3. {1,0,1,2}
  4. {5,0,3,4}
Determine the domain and range of a relation

For each relation below, find the domain and range.

  1. R={(13,7),(2,4),(0,0),(10,6),(8,7)}
  2. R={(1,1),(1,4),(1,6),(2,21),(4,15),(6,2),(6,10)}
  3. R={(4,0),(3,1),(4,0),(1,1)}
  4. R={(2,1),(1,4),(3,5),(0,5)}
Answer
  1. Domain: {13,0,2,8,10}; Range: {0,4,6,7}
  2. Domain: {1,1,2,4,6}; Range: {10,4,1,2,15,21}
  3. Domain: {4,3,1}; Range: {1,0,1}
  4. Domain: {3,2,1,0}; Range: {5,1,4,5}
Determine the domain and range of a relation using a table

For each relation below, determine the domain and range.

  1. xy31023011416510611
  1. xy61353131122180626
  1. xy442232333310101414
Answer
  1. Domain: {3,2,0,1,5,6}; Range: {10,1,3,4,6,10,11}
  2. Domain: {6,5,3,2,1,0,2}; Range: {11,6,2,13,31}
  3. Domain: {4,2,3,10,14}; Range: {14,10,3,2,2,3,4}
Determine if a relation is a function

Determine if the following relations are functions:

  1. R={(13,7),(2,4),(0,0),(10,6),(8,7)}
  2. R={(1,1),(1,4),(1,6),(2,21),(4,15),(6,2),(6,10)}
  3. R={(4,0),(3,1),(4,1),(1,1)}
  4. R={(2,1),(1,4),(3,5),(0,5)}
  5. R={(17,3),(4,2),(2,0),(6,10),(7,8)}
  6. R={(0,3),(0,5),(0,7),(3,22),(5,16),(7,3),(7,11)}
  7. R={(5,1),(4,0),(3,1),(2,2)}
  8. R={(3,0),(2,3),(2,4),(1,5)}
Answer
  1. Function
  2. Not a function
  3. Not a function
  4. Function
  5. Function
  6. Not a function
  7. Function
  8. Not a function
Evaluate a function represented with ordered pairs

For each function below, evaluate the following: f(1),f(0),f(3)

  1. f={(1,3),(0,5),(3,16)}
  2. f={(4,5),(1,2),(0,5),(3,5)}
  3. f={(13,7),(1,1),(2,4),(0,0),(3,4)(10,6),(8,7)}
  4. f={(5,1),(4,0),(3,1),(2,2),(1,12),(0,4),(3,2)}
  5. f={(3,0),(2,3),(1,9),(0,4),(1,5),(3,14),(9,2)}
Answer
  1. f(1)=3;f(0)=5;f(3)=16
  2. f(1)=2;f(0)=5;f(3)=5
  3. f(1)=1;f(0)=0,f(3)=4
  4. f(1)=12;f(0)=4;f(3)=2
  5. f(1)=9;f(0)=4;f(3)=14
Evaluate functions defined using an equation

For each function below, evaluate the following: f(3),f(0),f(5)

  1. f(x)=2x+1
  2. f(x)=x2+1
  3. f(x)=x+4
  4. f(x)=|x|+5
  5. f(x)=17
  6. f(x)=3x4
  7. f(x)=2x22
  8. f(x)=x+4+9
  9. f(x)=2|x|+3
  10. f(x)=3
Answer
  1. f(3)=5;f(0)=1,f(5)=11
  2. f(3)=10;f(0)=1;f(5)=26
  3. f(3)=1;f(0)=2;f(5)=3
  4. f(3)=8;f(0)=5;f(5)=10
  5. f(3)=17;f(0)=17;f(5)=17
  6. f(3)=13;f(0)=4;f(5)=11
  7. f(3)=16;f(0)=2;f(5)=48
  8. f(3)=10;f(0)=11;f(5)=12
  9. f(3)=3;f(0)=3;f(5)=7
  10. f(3)=3;f(0)=3;f(5)=3
Find the domain and range of a function defined using an equation

Find the domain and range for each of the functions below:

  1. f(x)=2x+1
  2. f(x)=x2+1
  3. f(x)=x+4
  4. f(x)=|x|+5
  5. f(x)=17
  6. f(x)=3x4
  7. f(x)=2x22
  8. f(x)=x+4+9
  9. f(x)=2|x|+3
  10. f(x)=3
Answer
  1. Domain: (,); Range: (,)
  2. Domain: (,); Range: (1,)
  3. Domain: x4; Range: y0
  4. Domain: (,); Range: y5
  5. Domain: (,); Range: y=17
  6. Domain: (,); Range: (,)
  7. Domain: (,); Range: (2,)
  8. Domain: x4; Range: y9
  9. Domain: (,); Range: y3
  10. Domain: (,); Range: y=3

This page titled 2.1E: Exercises is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Stanislav A. Trunov and Elizabeth J. Hale.

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