Begin by graphing f(x)=log_{2}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. g(x)=frac{1}{2}log_{2}x

boitshupoO 2021-01-10 Answered
Begin by graphing
f(x)=log2x
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.
g(x)=12log2x
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Expert Answer

odgovoreh
Answered 2021-01-11 Author has 107 answers

Step 1
For the following Logarithmic function defined by
f(x)=log2x
Graphing Logarithmic function given in equation requires setting up table of coordinates, so that
Table of coordinates of the Logarithmic function f(x)=log2xxf(x)=y=log2x(x, y)1f(1)=y=log2(1)  2y=1=20  y=0(1, 0)2f(2)=y=log2(2)  2y=2=21  y=1(2, 1)4f(4)=y=log2(4)  2y=4=22  y=2(4, 2)8f(8)=y=log2(8)  2y=8=23  y=3(8, 3)16f(16)=y=log2(16)  2y=16=24  y=4(16, 4)32f(32)=y=log2(32)  2y=32=25  y=5(32, 5)64f(64)=y=log2(64)  2y=64=26  y=6(64, 6)
Step 2
We plot the following points between (x, y) determined from the table of coordinates and connect them with the continuous curve which represent the Logarithmic function f(x)=log2x as shown in Figure (1)
Figure (1) represent the graph of Logarithmic function f(x)=log2x
image
Step 3
Note that:
The y-axis which represented by the equation x=0 is the vertical asymptote, so that the curve approches, but never touches the positive portion of the y-axis as shown in figure (1).
The domain of f(x)=log2(x) is all positive real numbers x  (0 ) and the range is all real numbers y  (, )
Step 4
To graph the Logarithmic function g(x)=12log2(x), we vertically shri
the graph of the function f(x)=log2(x) because 0 < 12 < 1 (f(x)=log2(x) Vertically shri
to g(x)=12log2(x)), then the Logarithmic function f(x)=log2(x<

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