Question 469108: Examine the leading term and determine the far-left and far-right behavior of the graph of the polynomial function P(x)=-2x^8-5x^5+9x^3-7.
a.can't be determined
b.down to far left,down to far right
c.down to far left,up to far right
d.up to far left,up to far right
e.up to far left,down to far right
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Examine the leading term and determine the far-left and far-right behavior of the graph of the polynomial function P(x)=-2x^8-5x^5+9x^3-7.
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-2x^8 determines what happens
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As x goes to -oo, -2x^8 goes down
As x goes to +oo, -2x^8 goes down
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Ans: b
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Cheers,
Stan H.
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a.can't be determined
b.down to far left,down to far right
c.down to far left,up to far right
d.up to far left,up to far right
e.up to far left,down to far right
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! The leading term is -2x^8.
The value based on the leading term will always be negative.
The leading term will always be dominant as x gets larger because it is raising x to the 8th power while the remainder of the equation only raises x to lower powers.
If x is smaller, then the other values can predominate.
For example, when x = 1, -2x^8 is equal to -2 while -5x^5 is equal to 5.
The fact that the exponent of x^8 is even means that x^8 will always be positive.
Since x^8 is multiplied by -2, this means that -2x^8 will always be negative.
At any rate, as x gets larger, -2x^8 will be the dominant factor and the graph will take on that value more and more.
This means that the left and the right of the equation will be pointing down.
That would be selection B.
A graph of this equation is shown below:
Apparently it didn't take too long for -2x^8 to predominate.
the table below shows selected values of x and their corresponding values of y after x has been processed through the equation.
x y
-5 -766757
-2 -431
-1.5 -50.6640625
-1 -13
-0.5 -7.9765625
0 -7
0.5 -6.0390625
1 -5
1.5 -65.8515625
2 -607
5 -795757
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