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 functions domain and range. g(x)= -2log_{2}x

Albarellak 2021-01-28 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 functions domain and range. g(x)= 2log2x
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brawnyN
Answered 2021-01-29 Author has 91 answers

Step 1 For the following Logarithmic function defined by 1) f(x)= log2x Graphing Logarithmic function given in equation (1) requires setting up table of coordinates, so that

xf(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, ) andthe range is all real numbers y  (, ).

Step 4 To graph the Logarithmic function g(x)= 2 log2<

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