Question

transformation question; details inside, please help!

Answer 1

What is the transformation that occurs to the equation \[y = (\frac{ 1 }{ 2 })^{x}\] if the equation changes to \[y = (\frac{ 1 }{ 2 })^{-x + 1}\]

Answer 2

@zepdrix

Answer 3

Rule of exponents:
\[\Large \color{royalblue}{a^{x+y}=a^x\cdot a^y}\]

Let's us write our function like this,
\[\Large \left(\frac{1}{2}\right)^{-x+1} \qquad=\qquad \left(\frac{1}{2}\right)^{-x}\cdot \left(\frac{1}{2}\right)^{1}\]

Answer 4

Understand that part? :)

Answer 5

yes

Answer 6

Its very important to note that : \(\left(\frac{1}{2}\right)^{-x+1}=\left(\frac{1}{2}\right)^{-(x-1)}\)

The negative sign before the x signifies a horizontal reflection in the y-axis and the "-1)" signifies a horizontal translation one unit to the right! :-)