SOLUTION: For each of the following functions, i) describe the transformations compared to y = x2, il) graph the function by making a table of values a. y = (x + 3)2-2

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Question 1202237: For each of the following functions, i) describe the transformations compared to y = x2,
il) graph the function by making a table of values
a. y = (x + 3)2-2
Found 2 solutions by mananth, greenestamps:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

y+=+%28x+%2B+3%29%5E2-2
Plug any value for x , find y and plot the graph
x=0, 3^2-2 =7 y=7 (0,7)
x=-1, 2^2-2 =2 y=2 (-1,2)
x=2, 25-2 = 23 (2,23)
x=-3 0-2 =-2 (-3,2)
x shifts left 3 units
y shifts down 2 units
.





Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Graphing the function using a table of values is busy work; and you learn nothing by doing it. Since the assignment tells you to do it, go ahead and do it... but I'm not going to spend time doing it in my response.

And determining the transformations by making a table of values, as the response from the other tutor does, is not good mathematics. You want to understand how the transformations are determined directly from the given function.

In evaluating the given function for a given value of x, you would first add 3 to x; then after squaring (which is what the basic function does), you would subtract 2. That order of operations in evaluating the function for a given value of x tells you that the first transformation is the "+3" and the second transformation is "-2".

The basic function is y=x^2:

graph%28400%2C400%2C-5%2C5%2C-10%2C20%2Cx%5E2%29

The "x+3" shifts the graph 3 units left:

graph%28400%2C400%2C-5%2C5%2C-10%2C20%2Cx%5E2%2C%28x%2B3%29%5E2%29

The "-2" shifts the graph 2 units down:

graph%28400%2C400%2C-5%2C5%2C-10%2C20%2Cx%5E2%2C%28x%2B3%29%5E2%2C%28x%2B3%29%5E2-2%29

The sequence of transformations, directly from the given function, is...

ANSWER: (1) left 3; (2) down 2