SOLUTION: 6x^2 - 28x + 16 x^4 + 2x^3 - 3x - 6 x^8 - 1 If I am doing it correctly and according to the book; the answer should be b. Is this correct?

Question 144117: 6x^2 - 28x + 16
x^4 + 2x^3 - 3x - 6
x^8 - 1
If I am doing it correctly and according to the book; the answer should be b. Is this correct?
Found 3 solutions by jim_thompson5910, solver91311, stanbon:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Sometimes the best way to do this is to graph. So here's the graph of

Graph of

Now when we want to find , simply replace each "x" of to get

Don't worry about simplification. Now let's graph

Graph of

So together they look like

Graph of (red) and graph of (green)

So R(x+2) shifts the original function R(x) 2 units to the left. So the answer is a). Note: check the answer and make sure that it's from the right section/chapter.
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!
I certainly hope your book did not tell you the answer is b.

Think about it: In the second definition of the function, you would have to put an x value that is 2 less than the x value that would give you the same function value in the first definition.

For example: For R(x) = 0, x = or , but for R(x+2) = 0, x = or .

Everything shifts 2 units to the right. Answer c.

See below: The green graph is

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Let R(x) = x^2 - 7/x^2 + 1; what happens to R(x) if we now have R(x+2)?
a. It shifts 2 units to the left
b. It shifts 2 units up
c. It shifts 2 units to the right
d. It remains stationary; there is no effect of adding 2 to x
----------------
Answer: a
Cheers,
Stan H.

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