Question

Write a rule for the G that represents the indicated transformation of the graph of f

Answer 1

Recall that we are given a function and we are told to apply some transformations to it. First, let us forget about the given function and just call it f.

If we want to apply a vertical translation, we simply do the following

`f+D`

This transformation would move the function f a total of D units. If the sign of D is positive, it would move D units up, and it would move D units down otherwise.

Now, if we have a function f and apply a vertical stretch, we simply multiply the function by the stretching factor as follows

`K\cdot f`

where K is the stretching factor.

Then, we start with our function f. We are told that we will apply a vertical translation of 2 units down. Then D=-2. So we get

`\log _5x\text{ -2}`

Now, to this function we need to apply a vertical stretch of factor 8. That is, take K=8. So we get that our final function is

`8\cdot(\log _5x\text{ -2) = 8}\cdot\log _5x\text{ -8}\cdot2\text{ = 8}\cdot\log _5x\text{ -16}`

Then the final function would be

`8\cdot\log _5x\text{ -16}`