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Mathematics LibreTexts

1.0E Exercises

  • Page ID
    10622
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    For the following exercises, (a) determine the domain and the range of each relation, and (b) state whether the relation is a function.

     

    Exercise \(\PageIndex{1}\)

     

    \(x\) \(y\) \(x\) \(y\)
    -3 9 1 1
    -2 4 2 4
    -1 1 3 9
    0 0    
    Answer

    a. Domain = {\(−3,−2,−1,0,1,2,3\)}, range = {\(0,1,4,9\)}

    b. Yes, a function

     

    Exercise \(\PageIndex{2}\)

     

    \(x\) \(y\) \(x\) \(y\)
    1 -3 1 1
    2 -2 2 2
    3 -1 3 3
    0 0    
    Answer

    a. Domain = {\(0,1,2,3\)}, range = {\(−3,−2,−1,0,1,2,3\)}

    b. No, not a function

     

    Exercise \(\PageIndex{3}\)

    \(x\) \(y\) \(x\) \(y\)
    3 3 15 1
    5 2 21 2
    8 1 33 3
    10 0    
    Answer

    a. Domain = {\(3,5,8,10,15,21,33\)}, range = {\(0,1,2,3\)}

    b. Yes, a function

     

    For the following exercises, find the values for each function, if they exist, then simplify.  

    a. \(f(0)\) b. \(f(1)\) c. \(f(3)\) d. \(f(−x)\) e. \(f(a)\) f. \(f(a+h)\)

    Exercise \(\PageIndex{4}\)

    \(f(x)=5x−2\)

    Answer

    a. \(−2\) b. \(3\) c. \(13\) d. \(−5x−2\) e. \(5a−2\) f. \(5a+5h−2\)

    Exercise \(\PageIndex{5}\)

    \(f(x)=\frac{2}{x}\)

    Answer

    a. Undefined b. \(2\) c. \(23\) d. \(−\frac{2}{x}\) e \(\frac{2}{a}\) f. \(\frac{2}{a+h}\)

    Exercise \(\PageIndex{6}\)

    \(f(x)=\sqrt{6x+5}\)

    Answer

    a. \(\sqrt{5}\) b. \(\sqrt{11}\) c. \(\sqrt{23}\) d. \(\sqrt{−6x+5}\) e. \(\sqrt{6a+5}\) f. \(\sqrt{6a+6h+5}\)

    Exercise \(\PageIndex{7}\)

    \(f(x)=|x−7|+8\)

    Answer

    a. \(15\) b. \(14\) c. \(12\) d. \(|x+7|+8\) e. \(|a−7|+8\) f. \(|a+h−7|+8\)

    Exercise \(\PageIndex{8}\)

    \(f(x)=\frac{x−2}{3x+7}\)

    Answer

    a. \frac{-2}{7}  b. \(-.1\) c. \(\frac{1}{17}\) d. \(-\frac{x+2}{-3x+7}\) e \(\frac{a−2}{3a+7}\) f. \(\frac{a+h−2}{3a+3h+7}\)

    Exercise \(\PageIndex{9}\)

    \(f(x)=9\)

    Answer

    a. 9 b. 9 c. 9 d. 9 e. 9 f. 9

     

    For the following exercises, find the domain, range, and all zeros/intercepts, if any, of the functions.

     

    Exercise \(\PageIndex{10}\)

    \(g(x)=\sqrt{8x−1}\)

    Answer

    \(x≥\frac{1}{8};y≥0;x=\frac{1}{8}\); no y-intercept

    Exercise \(\PageIndex{11}\)

    \(f(x)=−1+\sqrt{x+2}\)

    Answer

    \(x≥−2;y≥−1;x=−1;y=−1+\sqrt{2}\)

    Exercise \(\PageIndex{12}\)

    \(g(x)=\frac{3}{x−4}\)

    Answer

    \(x≠4;y≠0\); no x-intercept; \(y=−\frac{3}{4}\)

    Exercise \(\PageIndex{13}\)

    \(g(x)=\sqrt{\frac{7}{x−5}}\)

    Answer

    \(x>5;y>0\); no intercepts

    Exercise \(\PageIndex{14}\)

    \(f(x)=\frac{x}{x^2−16}\)

    Answer

    \(x≠\pm 4\); \(x=0,y=0\)

     

     

     

    Contributors

    Gilbert Strang (MIT) and Edwin “Jed” Herman (Harvey Mudd) with many contributing authors. This content by OpenStax is licensed with a CC-BY-SA-NC 4.0 license. Download for free at http://cnx.org.

    Pamini Thangarajah (Mount Royal University, Calgary, Alberta, Canada)