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?

Algebra ->  Equations -> 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?      Log On


   

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) About Me  (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 R%28x%29=%28x%5E2+-+7%29%2F%28x%5E2+%2B+1%29


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%28x%5E2+-+7%29%2F%28x%5E2+%2B+1%29%29+ Graph of R%28x%29=%28x%5E2+-+7%29%2F%28x%5E2+%2B+1%29



Now when we want to find R%28x%2B2%29, simply replace each "x" of R%28x%29 to get

R%28x%2B2%29=%28%28x%2B2%29%5E2+-+7%29%2F%28%28x%2B2%29%5E2+%2B+1%29


Don't worry about simplification. Now let's graph R%28x%2B2%29=%28%28x%2B2%29%5E2+-+7%29%2F%28%28x%2B2%29%5E2+%2B+1%29


Graph of R%28x%2B2%29=%28%28x%2B2%29%5E2+-+7%29%2F%28%28x%2B2%29%5E2+%2B+1%29


So together they look like


Graph of R%28x%29=%28x%5E2+-+7%29%2F%28x%5E2+%2B+1%29 (red) and graph of R%28x%2B2%29=%28%28x%2B2%29%5E2+-+7%29%2F%28%28x%2B2%29%5E2+%2B+1%29 (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) About Me  (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 = sqrt%287%29 or -sqrt%287%29, but for R(x+2) = 0, x = -2%2Bsqrt%287%29 or -2-sqrt%287%29.

Everything shifts 2 units to the right. Answer c.

See below: The green graph is R%28x%2B2%29


Answer by stanbon(75887) About Me  (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.