SOLUTION: list the steps and explain the effect of each transformation to graph the function y=-3log(-2x+1)+4

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Question 1193235: list the steps and explain the effect of each transformation to graph the function
y=-3log(-2x+1)+4
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


y=-3log%28%28-2x%2B1%29%29%2B4

Rewrite the function:

y=-3log%28%28-2%28x-1%2F2%29%29%29%2B4

The order of transformations is the order of operations you would use to evaluate the expression for a given value of x:

(1) subtract 1/2 -- shifts the graph 1/2 unit to the right
(2) multiply by -2 -- flips the graph horizontally about the line x=1/2; and compresses the graph horizontally by a factor of 2
(3) multiply by -3 -- stretches the graph vertically by a factor of 3
(4) add 4 -- shifts the graph 4 units up

The basic function is log(x):

graph%28400%2C400%2C-2%2C10%2C-2%2C2%2Cln%28x%29%2Fln%2810%29%29

After the first transformation, the function is log(x-1/2); the graph is shifted 1/2 unit to the right.


red = log(x); green=log(x-1/2)

After the second transformation, the function is log(-2(x-1/2)); the graph is flipped horizontally about the line x=1/2 and compressed horizontally by a factor of 2.


red = log(x-1/2); green = log(-2(x-1/2))

After the third transformation, the function is -3log(-2(x-1/2)); the graph is flipped vertically about the y-axis and stretched vertically by a factor of 3.


red = log(-2(x-1/2)); green = -3log(-2(x-1/2))

After the fourth transformation, the function is -3log(-2(x-1/2))+4; the graph is shifted 4 units up.


red = -3log(-2(x-1/2)); green = -3log(-2(x-1/2))+4