grade 12 advanced functions question

Question

what transformational mapping takes the graph of y=log₃X to the graph y=log₃(81X²). Justify your answer.

Answer 1

Rewrite the transformed function using the properties of logarithms.  We do this so that we get a function that has a term similar to the original function.

 

y = log₃(81x²)

 

y = log₃(9² * x²)

 

y = 2log₃(9) + 2log₃x

 

y = 2(2) + 2log₃x

 

y = 2log₃x + 4

 

Based on this new form of the transformed equation, we shift the original function 4 units up, and stretch it vertically by a factor of 2.

Answer 2

y=log(81x*x).    base 3.     new function

 

y=log(81) to base 3 +2logx to base 3

 

y=4 +2log(x) to base 3

 

we are given the function y = log(x) to base 3

 

Each ordinate of the given function is to be multiplied by 2 and 4 added to this will give the new function