1) Find the inverse of \(f(x) = e^{x+1}\).
Compare each function to the parent function \(f(x) = \log_5x\). Describe the transformations.
2) \(g(x) = 3 \log_5 \;x\)
3) \(h(x) = \frac{1}{2} \log_5\;x +1\)
4) \(k(x) = -5 \log_5\; (x - 2)\)
5) \(j(x) = \log_5\;(x + 3) - 6\)
For #6 & 7, describe the transformation from the green graph, \(f(x) = \log_2\;x\) to the blue graph.
6)
7)
8) Describe the transformation from \(f(x) = \log_2\;x\) to \(g(x)\) and \(h(x)\).
Graph each function and state the domain, range and vertical asymptote.
9) \(f(x) = \log_{3}\;(x)\)
10) \(h(x) = \log_2\;(x + 1) - 6\)
11) \(k(x) = -\large\frac{1}{2}\normalsize\log_6\;x\)
12) \(j(x) = 4\ln (x+9)\)
13) \(m(x) = -\ln (x - 5) + 1\)
14) \(n(x) = \large\frac{3}{2}\normalsize\log (x) -2\)
15) Describe and correct the error. Ed completed the table to transform the parent function to create \(f(x) = -\log_3\;(x) -3\).
Write the inverse of each function.
16) \(f(x) = 2\log_3(x - 11) - 2\)
17) \(f(x) = \frac{1}{2}\log_5(x) + 6\)
18) \(f(x) = 7\log_7(x-4)+2\)
19) \(f(x) = -4\Big(\frac{1}{2}\Big)^{(x+1)} - 6\)
20) \(f(x) = -2(6)^{x+1} - 11\)
21) \(f(x) =\frac{1}{3}\ln(x+1) - 3\)
22) \(f(x) = -\frac{5}{2}e^{x - 7} + 9\)
Review
23) If \(b^3(b^4)^2 = b^x\), what is the value of \(x\)?
24) Expand or contract the expression \(\ln (7) - \ln (49)\).
Solution Bank