Question 1129864

 a.
to describe the transformation that have been applied to given exponential function, recall: 

{{{y=a*b^(x-h)+v}}} where {{{a}}} is the vertical transformation, {{{h}}} is the horizontal shift, and {{{v }}}is the vertical shift


if given the graph of {{{F(x)=2^x }}} and obtain the graph {{{f(x)=2^(x+1)-3}}}

based on this equation, you see that

{{{h = -1}}} and it means {{{F(x)}}} has been shifted {{{one }}}unit to the {{{left }}}

and, {{{v = -3}}} means {{{F(x) }}}has been shifted {{{three}}} units {{{down}}}



b. 
what is the Domain & Ranger of {{{f(x)=2^(x+1)-3}}}? 

Domain:  {{{R}}} (all real numbers)

Range:   { {{{f(x)}}} element {{{R}}} : {{{f(x) > -3}}} }



c. what is the equation of the asymptote for the graph of {{{f(x)=2^(x+1)-3}}}?


{{{lim(x->-infinity)}}}{{{ (2^(x + 1) - 3) = -3}}}

Horizontal asymptote: {{{y=-3}}}


{{{ graph( 600, 600, -10, 10, -10, 10, 2^x, 2^(x+1)-3,-3) }}}