5.5: Function- Answers to the Homework Exercises

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Introductions to Functions

All are functions, except B. and G. because they fail the vertical line test

domain: $(−∞, 0) ∪ (0, ∞)$; $t$ is the independent variable, $s(t)$ is the dependent variable

domain: $(−∞, −1) ∪ (−1, 4) ∪ (4, ∞)$; $x$ is the independent variable, $f(x)$ is the dependent variable

domain: $(−∞, \dfrac{5}{4}]$; $x$ is the independent variable, $f(x)$ is the dependent variable

domain: $[16, ∞)$; $x$ is the independent variable, $f(x)$ is the dependent variable

domain: $(−∞, ∞)$; $t$ is the independent variable and its units are seconds, $h(t)$ is the dependent variable and its units are meters

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.

$g(0) = −4;\: (0, −4)$

$f(−6) = −7;\: (−6, −7)$

$f(10) = 13;\: (10, 13)$

$w(−2) =\dfrac{9}{4};\: \left(−2,\dfrac{9}{4}\right)$

$p(4) = −60;\: (4, −60)$

$g(2) = −\dfrac{3}{25};\: \left(2, −\dfrac{3}{25}\right)$

$f(10) = 7;\: (10.7)$

$w(−5) = 5;\: (−5, 5)$

$p(5) = −4;\: (5, −4)$

$k(2) = −32;\: (2, −32)$

$−64x^3 + 2$

$2| − 3t^2 − 1| + 2$

$5^{−3−x}$

$3 · 2^{a/4+3}$

$t^4+t^2$

Linear Functions

$f(x)=\dfrac{1}{5}x+\dfrac{7}{5}$

1. $1.85$; dollars per mile
2. $50$; dollars
3. $C(x)=1.85x+50$

$clipboard_e49b2bd88d210af33451b969209a0453d.png$
Figure 5.5.1

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Figure 5.5.2

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Figure 5.5.3

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Figure 5.5.4

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Figure 5.5.5

$E(t)=360t$

$C(t)=80t+50$, where $0<t\leq 8$

$C(p) = 0.035p + 1.50$; 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

$82$

$5$

$1$

$\dfrac{1}{5}$

$-x^3-4x-2$

$4x^3+25x^2+25x$

$2$

$-43$

$27$

$-x^3+2x^2-3$

$t^4+8t^2+2$

$-155$

$103$

$-2x+9$

$\dfrac{32+23n-n^3}{8}$

$4$

$-50$

$16x^2+12x-4$

$4x^3$

$-16t-5$

$147$

$t$

$27t^3-108t^2+141t-60$

Library of Functions

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

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