2.11 · Logarithmic Functions

Try each one on paper first, then tap to check.

1. 1.

   Sketch the transformation of $f(x) = \log_5 x$ and label it: $f(x) = 3\log_5(x+2) - 4$
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2. 2.

   Sketch the transformation of $f(x) = \log_5 x$ and label it: $g(x) = 3\log_5(3-x) + 1$
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3. 3.

   Sketch the transformation of $f(x) = \log_5 x$ and label it: $h(x) = -\log_5(x-3) - 2$
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4. 4.

   Find the asymptote, domain, range, and end behavior. Sketch a graph. $f(x) = \ln(x-3) + 5$
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5. 5.

   Find the asymptote, domain, range, and end behavior. Sketch a graph. $f(x) = -2\log_2(x+3) - 6$
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6. 6.

   Find the asymptote, domain, range, and end behavior. Sketch a graph. $f(x) = \log_6(8-x) + 1.5$
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7. 7.

   Find the asymptote, domain, range, and end behavior. Sketch a graph. $f(x) = -\log(2x-5)$
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8. 8.

   Find the asymptote, domain, range, and end behavior. Sketch a graph. $f(x) = 455\log_9(x+376) - 543$
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9. 9.

   Find the asymptote, domain, range, and end behavior. Sketch a graph. $f(x) = -3\ln(10-x)$
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10. 10.

    Write a logarithmic function with this end behavior:
    $x\to\infty,\ f(x)\to\infty$ and $x\to -6^+,\ f(x)\to -\infty$
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11. 11.

    Write a logarithmic function with domain $(-\infty, 8)$.
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12. 12.

    (Calculator) Find the asymptote, domain, range, and end behavior: $f(x) = \log(|x+4|) - 10$
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13. 13.

    (Calculator) Find the asymptotes, domain, range, and end behavior: $f(x) = -3\ln\!\left(\dfrac{x+7}{x}\right)$
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14. 14.

    $h$: when the input is tripled, the output increases by 1. Which graph could be $h(x)$? (A) steep line through origin (B) shallow line through origin (C) square-root-shaped curve starting at origin (D) curve with VA $x = 0$ through $(1,0)$, rising slowly
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15. 15.

    Which function could have this end behavior? $x\to 10^-,\ f(x)\to\infty$; $x\to -\infty,\ f(x)\to -\infty$
    (A) $f(x) = -3\ln(x-10)+5$
    (B) $g(x) = -2\log(5-x)+10$
    (C) $h(x) = -\log_3(10-x)-5$
    (D) $j(x) = \log(10-x)+4$
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16. 16.

    (Calculator) If $\log_{0.2}(x+2) < \log_{0.04}(x+2)$, then $x$ lies in: (A) $(-\infty,-1)$ (B) $(-2,-1)$ (C) $(-1,\infty)$ (D) $(1,2)$
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