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

aflacatn 2021-08-15 Answered
For y=log3(x+2) a. Use transformations of the graphs of y=log2x and y=log3x to graph the given functions. b. Write the domain and range in interval notation. c. Write an equation of the asymptote.
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saiyansruleA
Answered 2021-08-16 Author has 110 answers
Step 1
a) Stert from the graph of the parent function f(x)=log3x.
As we can see the given function y=log3(x+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=log3(x+2) will be the same as the graph of the parent function f(x)=log3x shifted 2 units left.
See the graph in the picture below:

Step 2
b) The domain of the function y=log3(x+2) is the interval: (2,+)
The range of the function y=log3(x+2) is the interval (,+)
c) The vertical asymptote of the graph of this function is the line x=2
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