Question 1137988
The graph of 
{{{f(x) = (1/4)^ (-x) }}}is reflected about the y-axis and compressed vertically by a factor of 
{{{1/5}}}. 
What is the equation of the new function, {{{g(x)}}}? 

The basic parent function of any exponential function is {{{f(x) = b^x}}}, where b is the base. 
Because an exponential function is simply a function, you can transform the parent graph of an exponential function in the same way as any other function: 

 {{{f(x) =a* b^(x-h) +k }}}

where {{{a}}} is the vertical transformation,{{{ h}}} is the horizontal shift, and {{{k}}} is the vertical shift.


in your case given {{{1/5}}} is value of {{{a}}}, so

{{{g(x)=(1/5)(1/4)^ (-x)}}}


{{{drawing( 600, 600, -10, 10, -10, 10,
locate(2,3,f(x)=(1/4)^(-x)),locate(0.2,4,g(x)=(1/5)(1/4)^(-x)),
 graph( 600, 600, -10, 10, -10, 10, (1/4)^ (-x),(1/4)^ (-x), (1/5)(1/4)^ (-x))) }}}