SOLUTION: y=2(1/2)^(x+6) -7 state transformations, then graph the parent function and transformed functions, clearly plotting the KEY points, also draw and label the asymptotes

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Question 1189963: y=2(1/2)^(x+6) -7
state transformations, then graph the parent function and transformed functions, clearly plotting the KEY points, also draw and label the asymptotes



Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
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y=2(1/2)^(x+6) -7

state transformations, then graph the parent function and transformed functions,
clearly plotting the KEY points, also draw and label the asymptotes
~~~~~~~~~~~~~~~~~~~

The parent function is  y = .


The transformations are 


    1)  first, we shift the parent function 6 units to the left;

    2)  then we stretch y-axis with the coefficient 2;

    3)  finally, we shift the function's plot 7 units down vertically.


To make plot, use your graphing calculator.


You also can use free of charge plotting tool at this web-site www.desmos.com .


You should do sequentially these plots


    (1)  y =       (parent function).


    (2)  y = ;


    (3)  y = ;


    (4)  y = .


Using plotting tool  www.desmos.com,  you may have all these plots in one screen.


Now go to web-site  www.desmos.com and get there the plotting tool.


After that, print formula for function (1) in the first line: you will see the plot of the first function immediately.


After that, print formula for function (2) in the second line: you will see the plot of the second function immediately.


After that . . . . and so on . . . to the end . . . 


Do you notice that I'm running your hand over the keyboard?



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


A note to add to the response from the other tutor....

The order of transformations can be determined by looking at how you would evaluate the function for a given value of x, using PEMDAS order of operations.

(1) P (parentheses): add 6 to x (horizontal shift 6 to the left)
(2) M (multiplication): multiply by 2 (vertical stretch by a factor of 2)
(3) S (subtraction): subtract 7 (vertical shift of -7)

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