For y=2+ \log_{3}x. a) Use transformations of the graphs of y=\log_{2}x

a2linetagadaW

a2linetagadaW

Answered question

2021-08-14

For y=2+log3x.
a) Use transformations of the graphs of y=log2x and y=log3x o graph the given functions.
b) Write the domain and range in interval notation.
c) Write an equation of the asymptote.

Answer & Explanation

odgovoreh

odgovoreh

Skilled2021-08-15Added 107 answers

Step 1
a)Start from the graph of the parent function f(x)=log3x
As we can see the given function y=log3x+2 can be expressed in terms of the parent function f as y=f(x)+2
This indicates that the graph of the function y=log3x+2 will be the same as the graph of the parent function f(x)=log3x shifted 2 units upward.
See the graphs in the picture below:
Step 2
b) The domain of the function y=log3x+2 is the interval: (0,+)
The range of the function y=log3x+2 is the interval (,+)
c) The vertical asymptote of the graph of this function is the line x=0

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