Functions and graphing calculator help

Question

y=log₃(x)+1

a)To use a graphing calculator to graph this function, what equivalent function must be used?

b) what is the equation of the vertical asymptote?

Answer 1

a)

 

First, we need to write the function in another way so that we have no specific bases for the logs.

 

y - 1 = log₃(x)

 

 

The solution to a log is the exponent of the log's base number.  The base number is 3.

 

3^{(y - 1)} = x

 

3^y / 3 = x

 

3^y = 3x

 

 

Log both sides of the equations and bring the exponent down as the coefficient of the logs

 

 

ylog(3) = log(3x)

 

y = log(3x) / log(3)

 

 

Now you can easily graph this function on a graphing calculator, since you have no specific bases for the logs.

 

 

b)

 

Use the graphing calculator to find the vertical asymptote.  The vertical asymptote is the x value the graph gets closer to but never touches.