Question

For y= -log_{2}x. a) Use transformations of the graphs of y=log_{2}x and y=log_{3}x o graph the given functions. b) Write the domain and range in interval notation. c) Write an equation of the asymptote.

Transformations of functions
ANSWERED
asked 2021-02-11
For \(\displaystyle{y}=\ -{{\log}_{{{2}}}{x}}\).
a) Use transformations of the graphs of \(\displaystyle{y}={{\log}_{{{2}}}{x}}\) and \(\displaystyle{y}={{\log}_{{{3}}}{x}}\) o graph the given functions.
b) Write the domain and range in interval notation.
c) Write an equation of the asymptote.

Answers (1)

2021-02-12
Step 1
a) Start from the graph of the parent function \(\displaystyle{f{{\left({x}\right)}}}={{\log}_{{{2}}}{x}}\).
As we can see the given function \(\displaystyle{y}=\ -{{\log}_{{{2}}}{x}}\) can be expressed in terms of the parent function f as \(\displaystyle{y}=\ -{f{{\left({x}\right)}}}\)
This indicates that the graph of the function \(\displaystyle{y}=\ -{{\log}_{{{2}}}{x}}\) will be the same as the graph of the parent function \(\displaystyle{f{{\left({x}\right)}}}={{\log}_{{{2}}}{x}}\) reflected through the x-axis.
See the graphs in the picture below:
image
Step 2
b) The domain of the function \(\displaystyle{y}=\ -{{\log}_{{{2}}}{x}}\) is the interval: \(\displaystyle{\left({0},\ +\infty\right)}\)
The range of the function \(\displaystyle{y}=\ -{{\log}_{{{2}}}{x}}\) is the interval \(\displaystyle{\left(-\infty,\ +\infty\right)}\)
c) The vertical asymptote of the graph of this function is the line \(\displaystyle{x}={0}\)
0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours
...