Logarithmic/asymptote
In exercise 53-56, begin by graphing f(x) = log2 x. Then use transformations of this graph to graph the given function. What is the vertical asymptote? Use the graphs to determine each function's domain and range.
56. h(x) = 2 + log2 x
The figure show the graph of f(x) = log x. In exercises 59-64, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range.
60. g(x) = log(x-2)
64. g(x) = 2 - logx
The figure shows the graph of f(x) = ln x. In exercises 65-74, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range.
68. h(x) = ln(1/2x)
72. h(x) = ln(-x)
In exercises 75-80, find the domain of each logarithmic function.
76. f(x) = log5(x+6)
80. f(x) = ln(x-7)^2
In exercises 81-100, evaluate or simplify each expression without using a calculator.
84. log 10^8
88. ln e
92. ln 1/e^7
96. ln e^13x
100. 10^log3sqrt x
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Solution Preview
In exercise 53-56, begin by graphing f(x) = log2 x. Then use transformations of this graph to graph the given function. What is the vertical asymptote? Use the graphs to determine each function's domain and range.
56. h(x) = 2 + log2 x
Answer: The graph is attached. The vertical asymtote is x = 0. The domain is (0, oo) and the range is (-oo, oo).
The figure show the graph of f(x) = log x. In exercises 59-64, use transformations of this graph to graph ...
Solution Summary
This post encompasses Logarithmic/asymptote.