Question 1158030


 find the relation to its parent graph for this: {{{y=-(2)^(x+5) -1}}}

{{{f(x) = a*e^(b(x-c)) + d}}}


{{{c}}} - Translate Graph {{{Horizontally}}}
When you subtract a positive number {{{c}}} from {{{x}}}, you are translating {{{horizontally}}} the graph of the function {{{c}}} units {{{to}}}{{{ the}}} {{{right}}}. 
When {{{c }}}is negative, you are translating {{{horizontally}}} the graph of the function {{{c}}} units {{{to}}}{{{ the}}}{{{ left}}}.


{{{b}}} - Horizontal {{{Stretching }}}or Compression
When you multiply {{{x}}} by a positive {{{b}}} you will be performing either a horizontal {{{compression}}} or horizontal {{{stretching}}} of the graph. 
If {{{0 < b < 1}}} you have a horizontal {{{compression}}} and if {{{b > 1}}} then you have a horizontal {{{stretching}}}. 
When {{{b}}} is {{{negative}}}, then this horizontal compression or horizontal stretching of the graph is followed by a {{{reflection}}} across the {{{y}}}-axis.

a - Vertical {{{Stretching}}} or Compression
When you multiply a function by a positive {{{a}}} you will be performing either a vertical compression or vertical stretching of the graph. 
If {{{0 < a < 1}}} you have a vertical compression and if {{{a > 1}}} then you have a vertical stretching. 
When {{{a}}} is negative, then this vertical compression or vertical stretching of the graph is followed by a reflection across the {{{x}}}-axis.
 

d - Translate Graph{{{ Vertically}}}

When you add a positive number {{{d }}}to a function, you are translating vertically the graph of the function {{{d}}} units upwards.
 When d is negative, you are translating vertically the graph of the function {{{d}}} units downwards.


{{{y=-(2)^(x+5) -1}}} compared to {{{f(x) = a*e^(b(x-c)) + d}}}

{{{a=-1}}}=>{{{a}}} is negative, then this {{{vertical}}}{{{ compression}}} or vertical stretching of the graph is followed by a reflection across the {{{x}}}-axis

{{{b=1}}}=> there is {{{no}}} a horizontal compression or horizontal stretching 

{{{c=-5}}}=>{{{c}}} is negative, you are translating horizontally the graph of the function {{{5}}} units to the left

{{{d=-1}}}=>{{{d}}} is negative, you are translating vertically the graph of the function {{{1}}} units downwards



{{{ graph( 600, 600, -10, 10, -10, 10, -(2)^(x+5) -1,2^x ) }}}