5.5: Function- Answers to the Homework Exercises

Intermediate Algebra for Science, Technology, Engineering, and Mathematics · LibreTexts

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    Introductions to Functions

    1. All are functions, except B. and G. because they fail the vertical line test
    1. domain: \((−∞, 0) ∪ (0, ∞)\); \(t\) is the independent variable, \(s(t)\) is the dependent variable
    1. domain: \((−∞, −1) ∪ (−1, 4) ∪ (4, ∞)\); \(x\) is the independent variable, \(f(x)\) is the dependent variable
    1. domain: \((−∞, \dfrac{5}{4}]\); \(x\) is the independent variable, \(f(x)\) is the dependent variable
    1. domain: \([16, ∞)\); \(x\) is the independent variable, \(f(x)\) is the dependent variable
    1. domain: \((−∞, ∞)\); \(t\) is the independent variable and its units are seconds, \(h(t)\) is the dependent variable and its units are meters
    1. domain: \((−∞, ∞)\); \(x\) is the independent variable and its units are the number of hearing aids, \(R(x)\) is the dependent variable and its units are dollars.
    1. \(g(0) = −4;\: (0, −4)\)
    1. \(f(−6) = −7;\: (−6, −7)\)
    1. \(f(10) = 13;\: (10, 13)\)
    1. \(w(−2) =\dfrac{9}{4};\: \left(−2,\dfrac{9}{4}\right)\)
    1. \(p(4) = −60;\: (4, −60)\)
    1. \(g(2) = −\dfrac{3}{25};\: \left(2, −\dfrac{3}{25}\right)\)
    1. \(f(10) = 7;\: (10.7)\)
    1. \(w(−5) = 5;\: (−5, 5)\)
    1. \(p(5) = −4;\: (5, −4)\)
    1. \(k(2) = −32;\: (2, −32)\)
    1. \(−64x^3 + 2\)
    1. \(2| − 3t^2 − 1| + 2\)
    1. \(5^{−3−x}\)
    1. \(3 · 2^{a/4+3}\)
    1. \(t^4+t^2\)

    Linear Functions

    1. \(f(x)=\dfrac{1}{5}x+\dfrac{7}{5}\)
      1. \(1.85\); dollars per mile
      2. \(50\); dollars
      3. \(C(x)=1.85x+50\)
    1. clipboard_e49b2bd88d210af33451b969209a0453d.png
      Figure 5.5.1
    1. clipboard_edee7f3c227dc4b6fa158ed44a53b0670.png
      Figure 5.5.2
    1. clipboard_e606e99554ad16c330d2e7437838ff40a.png
      Figure 5.5.3
    1. clipboard_e18d69e1f2c3f43998aa567ce05d496e2.png
      Figure 5.5.4
    1. clipboard_eb283e85e85649f9d16f683032767c772.png
      Figure 5.5.5
    1. \(E(t)=360t\)
    1. \(C(t)=80t+50\), where \(0<t\leq 8\)
    1. \(C(p) = 0.035p + 1.50\); it costs \($0.035\) per page to print; the fixed costs are \($1.50\) per book whether pages are printed or not

    Algebra of Functions

    1. \(82\)
    1. \(5\)
    1. \(1\)
    1. \(\dfrac{1}{5}\)
    1. \(-x^3-4x-2\)
    1. \(4x^3+25x^2+25x\)
    1. \(2\)
    1. \(-43\)
    1. \(27\)
    1. \(-x^3+2x^2-3\)
    1. \(t^4+8t^2+2\)
    1. \(-155\)
    1. \(103\)
    1. \(-2x+9\)
    1. \(\dfrac{32+23n-n^3}{8}\)
    1. \(4\)
    1. \(-50\)
    1. \(16x^2+12x-4\)
    1. \(4x^3\)
    1. \(-16t-5\)
    1. \(147\)
    1. \(t\)
    1. \(27t^3-108t^2+141t-60\)

    Library of Functions

    1. \(A ↔ i\); \(B ↔ h\); \(C ↔ d\); \(D ↔ b\); \(E ↔ a\); \(F ↔ g\); \(G ↔ f\); \(H ↔ c\); \(I ↔ e\)
    2. \(A ↔ g\); \(B ↔ d\); \(C ↔ f\); \(D ↔ c\); \(E ↔ e\); \(F ↔ i\); \(G ↔ a\); \(H ↔ h\); \(I ↔ b\)
    3. \(A, B, C, D, G, H, I → (−∞, ∞)\), \(E → (−∞, 0) ∪ (0, ∞)\), \(F → (0, ∞)\)

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