2.1E: Exercises
( \newcommand{\kernel}{\mathrm{null}\,}\)
Practice Makes Perfect
For each of the following relations, create a mapping diagram and table.
- R={(−17,3),(4,2),(2,0),(6,−10),(7,8)}
- R={(0,3),(0,−5),(0,7),(3,22),(5,16),(7,3),(7,−11)}
- R={(−5,−1),(−4,0),(−3,1),(−2,2)}
- R={(−3,0),(−2,3),(−2,4),(1,−5)}
For each relation below, determine the domain.
- R={(−17,3),(4,2),(2,0),(6,−10),(7,8)}
- R={(0,3),(0,−5),(0,7),(3,22),(5,16),(7,3),(7,−11)}
- R={(−5,−1),(−4,0),(−3,1),(−2,2)}
- R={(−3,0),(−2,3),(−2,4),(1,−5)}
- Answer
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- {−17,2,4,6,7}
- {0,3,5,7}
- {−5,−4,−3,−2}
- {−3,−2,1}
For each relation below, determine the range.
- R={(−17,3),(4,2),(2,0),(6,−10),(7,8)}
- R={(0,3),(0,−5),(0,7),(3,22),(5,16),(7,3),(7,−11)}
- R={(−5,−1),(−4,0),(−3,1),(−2,2)}
- R={(−3,0),(−2,3),(−2,4),(1,−5)}
- Answer
-
- {−10,0,2,3,8}
- {−11,−5,3,7,16,22}
- {−1,0,1,2}
- {−5,0,3,4}
For each relation below, find the domain and range.
- R={(−13,7),(2,4),(0,0),(10,6),(8,7)}
- R={(1,1),(−1,−4),(−1,6),(2,21),(4,15),(6,2),(6,−10)}
- R={(−4,0),(−3,−1),(−4,0),(−1,1)}
- R={(−2,1),(−1,4),(−3,5),(0,−5)}
- Answer
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- Domain: {−13,0,2,8,10}; Range: {0,4,6,7}
- Domain: {−1,1,2,4,6}; Range: {−10,−4,1,2,15,21}
- Domain: {−4,−3,−1}; Range: {−1,0,1}
- Domain: {−3,−2,−1,0}; Range: {−5,1,4,5}
For each relation below, determine the domain and range.
- xy−3−10−230−11416510611
- xy−613−531−3−11−22−180−62−6
- xy−442−23−2333−310−1014−14
- Answer
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- Domain: {−3,−2,0,1,5,6}; Range: {−10,−1,3,4,6,10,11}
- Domain: {−6,−5,−3,−2,−1,0,2}; Range: {−11,−6,2,13,31}
- Domain: {−4,2,3,10,14}; Range: {−14,−10,−3,−2,2,3,4}
Determine if the following relations are functions:
- R={(−13,7),(2,4),(0,0),(10,6),(8,7)}
- R={(1,1),(−1,−4),(−1,6),(2,21),(4,15),(6,2),(6,−10)}
- R={(−4,0),(−3,−1),(−4,1),(−1,1)}
- R={(−2,1),(−1,4),(−3,5),(0,−5)}
- R={(−17,3),(4,2),(2,0),(6,−10),(7,8)}
- R={(0,3),(0,−5),(0,7),(3,22),(5,16),(7,3),(7,−11)}
- R={(−5,−1),(−4,0),(−3,1),(−2,2)}
- R={(−3,0),(−2,3),(−2,4),(1,−5)}
- Answer
-
- Function
- Not a function
- Not a function
- Function
- Function
- Not a function
- Function
- Not a function
For each function below, evaluate the following: f(−1),f(0),f(3)
- f={(−1,3),(0,5),(3,16)}
- f={(−4,5),(−1,2),(0,5),(3,5)}
- f={(−13,7),(−1,−1),(2,4),(0,0),(3,4)(10,6),(8,7)}
- f={(−5,−1),(−4,0),(−3,1),(−2,2),(−1,12),(0,−4),(3,−2)}
- f={(−3,0),(−2,3),(−1,9),(0,4),(1,−5),(3,−14),(9,2)}
- Answer
-
- f(−1)=3;f(0)=5;f(3)=16
- f(−1)=2;f(0)=5;f(3)=5
- f(−1)=−1;f(0)=0,f(3)=4
- f(−1)=12;f(0)=−4;f(3)=−2
- f(−1)=9;f(0)=4;f(3)=−14
For each function below, evaluate the following: f(−3),f(0),f(5)
- f(x)=2x+1
- f(x)=x2+1
- f(x)=√x+4
- f(x)=|x|+5
- f(x)=−17
- f(x)=3x−4
- f(x)=2x2−2
- f(x)=√x+4+9
- f(x)=−2|x|+3
- f(x)=3
- Answer
-
- f(−3)=−5;f(0)=1,f(5)=11
- f(−3)=10;f(0)=1;f(5)=26
- f(−3)=1;f(0)=2;f(5)=3
- f(−3)=8;f(0)=5;f(5)=10
- f(−3)=−17;f(0)=−17;f(5)=−17
- f(−3)=−13;f(0)=−4;f(5)=11
- f(−3)=16;f(0)=−2;f(5)=48
- f(−3)=10;f(0)=11;f(5)=12
- f(−3)=−3;f(0)=3;f(5)=−7
- f(−3)=3;f(0)=3;f(5)=3
Find the domain and range for each of the functions below:
- f(x)=2x+1
- f(x)=x2+1
- f(x)=√x+4
- f(x)=|x|+5
- f(x)=−17
- f(x)=3x−4
- f(x)=2x2−2
- f(x)=√x+4+9
- f(x)=−2|x|+3
- f(x)=3
- Answer
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- Domain: (−∞,∞); Range: (−∞,∞)
- Domain: (−∞,∞); Range: (1,∞)
- Domain: x≥−4; Range: y≥0
- Domain: (−∞,∞); Range: y≥5
- Domain: (−∞,∞); Range: y=−17
- Domain: (−∞,∞); Range: (−∞,∞)
- Domain: (−∞,∞); Range: (−2,∞)
- Domain: x≥−4; Range: y≥9
- Domain: (−∞,∞); Range: y≤3
- Domain: (−∞,∞); Range: y=3