Question 933404
When we have an exponential equation of the form y=a^x ± k, then the graph will be moved up or down k units.


When we make a change in the exponent of the equation, a left or right shift happens. In general, for an exponential equation of the form y=a^(x±c) the graph of {{{y=a^x}}} will be moved left {{{c}}} units if {{{c}}} is positive, and right {{{c}}} units if {{{c}}} is negative.

If a {{{negative}}} {{{sign}}} is placed in front of an exponential function, then it will be reflected over the {{{x-axis}}}.

The graph of {{{y = -a^x}}} can be obtained by reflecting the graph of {{{y = a^x}}} in the x-axis.

The graph of the exponential equation {{{y = a^(-x)}}} can be obtained by reflecting the graph of {{{y = a^x}}} in the {{{y-axis}}.



to translated left {{{3}}} units means subtract {{{3}}}

{{{y=2^(x-3)}}}
 
to reflect about the x-axis place a {{{negative}}} {{{sign}}} in front

{{{y=-2^(x-3)}}}

to shifting it up {{{8}}} units means add  {{{8}}} 

{{{y=-2^(x-3)+8}}}

{{{ graph( 600, 600, -10, 10, -10, 10,2^x, -2^(x+3)+8) }}}