# Thread: Finding the Basic Function & Transformation question

1. ## Finding the Basic Function & Transformation question

this is the question i'm working on (trying too but not understanding much of what is going on)

Graph:
$\displaystyle y= -3(1/2) ^x+3 +4$

by first stating the basic function and then describing each transformation applied in order. Specifically describe what happens to the domain, range, asymptotes, y-intercept, and vertical stretch or compression.

How do I find the basic function? it is supposed to be $\displaystyle y= (1/2)^x$ but I don't get how you find that out.

( how do you get this information?) :

it is translated 3 units to the left.
it is vertically stretched by a factor of 3. < these are the answers from book.
it is reflected in the x-axis.
it is translated up 4 units.

2. I believe this is your function ...

$\displaystyle y = -\left(\dfrac{1}{2}\right)^{x+3} + 4$

the "parent" or most basic function being transformed is

$\displaystyle y = \left(\dfrac{1}{2}\right)^x$

first transformation is

$\displaystyle y = \left(\dfrac{1}{2}\right)^{x+3}$ ... the parent graph is shifted left 3 units.

the next transformation is

$\displaystyle y = -\left(\dfrac{1}{2}\right)^{x+3}$ ... the previous shifted graph is reflected over the x-axis

the last transformation is

$\displaystyle y = -\left(\dfrac{1}{2}\right)^{x+3} + 4$ ... the reflected graph is shifted up 4 units

in functional notation, this is the order of transformations depicted on the attached graphs ...

y = f(x)

y = f(x+3)

y = -f(x+3)

y = -f(x+3)+4

recommend you graph these one step at a time with your calculator ... it allows you to see the the transformations take place a step at a time.

3. Thanks!

before getting your reply I was going though the notes I made and I put it together with something i found on youtube.

g(x) = A(B(x-C))+D)

where A is: dilates graph vertically or flips over x-axis or both...
where B is: dilates graph horizontally over the x axis.
where C is : shifts graph left or right
where d is: shifts graph up or down.

and the negative sign indicates that is it has a reflection correct?

so it was becoming clearer...as I went along thanks though for you answer

The functional notation structure that you put would now make sense why they use that kind of form in the book. There are examples where they list the basic function and it continues down to a more complex function. NOW i see why. thanks again.