transformations of functions

[teddy7]

Hi,
I've been having difficulty correctly stating transformations of functions. The current question I'm working on is:


Beginning with the function f(x) = log_ax, state what transformations were used on this to obtain the functions given below:

1. 1. p(x) = - ⅝ log_ax
   2. r(x) = log_a(5 - x)
   3. t(x) = 2 log_a2x

For (a) my answer is: a reflection in the x axis, vertical compression by a factor of 5/8
(b): reflection in the y axis and shifted right 5 units
(c): vertical stretch by a factor of 2 and horizontally compressed by a factor of 2

Is this correct?

Thank you

 

[lookagain]

Beginning with the function f(x) = log_ax,
state what transformations were used on this to obtain the functions given below:

For (a) my answer is: a reflection in the x axis, vertical compression by a factor of 5/8

(b): reflection in the y axis and shifted right 5 units

(c): vertical stretch by a factor of 2 and horizontally compressed by a factor of 2

I agree with your stated transformations.

Here are some rewrites:

p(x) \(\displaystyle \ \)=\(\displaystyle \ \) -⅝*log_ax

r(x) \(\displaystyle \ \) =\(\displaystyle \ \) log_a(5 - x) \(\displaystyle \ \)=\(\displaystyle \ \) log_a(-x + 5) \(\displaystyle \ \)= \(\displaystyle \ \) log_a[-(x - 5)]

t(x) \(\displaystyle \ \)=\(\displaystyle \ \) 2*log_a(2x)