Question 186633: Hi there,
It would be great if someone could help me solve the following question as I am not too strong on transformations and it would be a huge help if someone could explain the solution to the following question.
Given the equation y=2^x, predict the equation for the graph that has been reflected in the y-axis, given a vertical stretch by a factor of 5, translated 2 units right and 5 units down.
Answer by vleith(2983)   (Show Source):
You can put this solution on YOUR website! Use this tool several times -->
http://72.3.253.76:8080/webMathematica3/quickmath/page.jsp?s1=graphs&s2=equations&s3=basic
First use it to plot y=2^x set x interval from -10 to 10 and y interval from -10 to 100
Look at that curve.
Now use the tool again. same interval. But this time plot y=2^(-x)
This second plot is the 'reflection' of the first plot across the y axis. Think of this as 'spinning' the curve around the y axis.
For the third plot, change the first plot to y = 5*(2^x)
Notice it has a steeper rise than the first plot, but has a 'similar shape'
To translate 2 units to the right, subtract 2 from the original value for x. All this does is 'slide' the original plot to the right. The shape is exactly the same as the original plot. Just shifted right. Remember, to shift right -- subtract. If you were asked to shift left, then add instead.
y = 2^(x+2)
Shifting x moves left and right. What do you think shifting y will do? Correct, it will move up or down.
The last question says shift is down 5. So we need to add 5 to y
y+5 = 2^x
Hope this plotting tool helps.
If you want to get a similar tool on your local machine, I recommend geogebra. It is free. Read more about getting it here --> http://collabvsl.wetpaint.com/page/Mathematics+Applications
It is free and works great
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