# How do you use the graph of f(x)=(7/2)^x to describe the transformation of g(x)=-(7/2)^(-x+6)?

Nov 11, 2017

See below.

#### Explanation:

$y = {\left(\frac{7}{2}\right)}^{x} \textcolor{w h i t e}{88} \left[1\right]$

Multiplying by a negative value causes a reflection in the line$y = 0$

$y = - {\left(\frac{7}{2}\right)}^{x} \textcolor{w h i t e}{88} \left[2\right]$

Multiply $x$ by $- 1$ causes a rotation about the y axis.

$y = - {\left(\frac{7}{2}\right)}^{- x} \textcolor{w h i t e}{88} \left[3\right]$

Adding a positive value $a$ to $x$ closes the curve, adding a negative value opens the curve, but the asymptote $y = 0$ remains.

$y = - {\left(\frac{7}{2}\right)}^{- x + 3} \textcolor{w h i t e}{88} \left[4\right]$

Graphs of each individual stage: