1. Need help with advanced functions homework

I did all the sample questions in class but they were nothing like the homework questions. Please answer any if you can

The sample questions didn't even have logs so I'm not sure how to do it with the log.

The questions asks me to: State the transformations applied to the following equation:

y=log_5x (log with base of 5 times variable x)

a) y=-log_5x

b) y=log_5(-x)

c) y=-log_5(-x)

I understand what is happening visually, but I don't know how to describe it verbally.

also I have this equation: y=-log_5(-x)

would the inverse be y=log_5(-x)

or would I also need to modify the variable... y=log_(x)?

The next is given the equation:

y= - 1 / 4 [ ( 2 ) ^ x - 4 ] + 5

Include a table and describe its features...

the sample questions were nothing like this one, didn't have a variable near the exponent which really throws me off

and finally: Solve 3^x= 7^2 using interpolations and logarithms .. this one im completely lost on

2. Re: Need help with advanced functions homework

Hello!

a) y=-log_5x

b) y=log_5(-x)

c) y=-log_5(-x)
a) This is called a reflection in the x- axis.
b) This is called a reflection in the y-axis.
c) Both: reflection in x and y axis.

also I have this equation: y=-log_5(-x)
I am not really sure and I don't want to give you an incorrect answer.

y= - 1 / 4 [ ( 2 ) ^ x - 4 ] + 5
Just state the transformations compared the parent function y = 2x

3. Re: Need help with advanced functions homework

also I have this equation: y=-log_5(-x)

would the inverse be y=log_5(-x)

or would I also need to modify the variable... y=log_(x)?
frequently if you have $y=f(x)$ you can solve the inverse function by solving for x in terms of y.

$y=f(x)=-\log_5(-x)$

$-y=\log_5(-x)$

$5^{-y}=-x$

$x=-5^{-y}$

and now we just change y to x on the right and label this the inverse function.

$f^{-1}(x)=-5^{-x}$

compare this with the inverse of $y=g(x)=\log_5(x)\Rightarrow g^{-1}(x)=5^x$

You can see that you have to account for both transformations to the function itself as well as transformations of its argument.