Question

Describe the transformations that must be applied to the parent function to obtain each of the following functions. a) f(x) = -3 log(2x) b) f(x) = log

Transformations of functions
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asked 2021-06-18

Describe the transformations that must be applied to the parent function to obtain each of the following functions.
a) \(\displaystyle{f{{\left({x}\right)}}}=-{3}{\log{{\left({2}{x}\right)}}}\)
b) \(\displaystyle{f{{\left({x}\right)}}}={\log{{\left({x}-{5}\right)}}}+{2}\)
c) \(\displaystyle{f{{\left({x}\right)}}}={\left(\frac{{1}}{{2}}\right)}{\log{{5}}}{x}\)
d) \(\displaystyle{f{{\left({x}\right)}}}={\log{{\left(−{\left(\frac{{1}}{{3}}\right)}{x}\right)}}}−{3}\)

Answers (1)

2021-06-19

Describe the transformation that made for the following terms. (a) \(\displaystyle{f{{\left({x}\right)}}}=-{3}{\log{{\left({2}{x}\right)}}}\)
\(a=-3, k=2\)
(b) \(\displaystyle{f{{\left({x}\right)}}}={\log{{\left({x}-{5}\right)}}}+{2}\)
\(d=5, c=2\)
(c) \(\displaystyle{f{{\left({x}\right)}}}=\frac{{1}}{{2}}{\log{{\left({5}{x}\right)}}}\)
\(a=\)\(\displaystyle\frac{{1}}{{2}}\), \(k=5\)
(d) \(\displaystyle{f{{\left({x}\right)}}}={\log{{\left(-{\left(\frac{{1}}{{3}}\right)}{x}\right)}}}-{3}\)
\(k=\)\(\displaystyle-{\left(\frac{{1}}{{3}}\right)}\), \(c=-3\)

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