Question 162729
your request:
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The functions are f(x)=2x^2+5x+7 and g(x)=x^3 + 2
The directions say evaluate the following: and identify the domain of each 
(f+g)(x)
I got x^3+2x^2+5x+9 but I dont know what the domain is.
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my answer:
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f+g(x) = f(x) + g(x)
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you got it right again.
domain is all x since nothing to make the answer imaginary or cause a division by 0.
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in general, if the domain is not specified, then the domain is whatever makes the range valid.
there will be 4 graphs.
scan down after each one to get the next plus any additional comments.
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graph of f+g(x) is graph of x^3+2x^2+5x+9 shown below
{{{graph(800,800,-9,9,-1000,1000,x^3+2*x^2+5*x+9)}}}
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graph of g-f(x) is graph of x^3-2x^2-5x-5 shown below
{{{graph(800,800,-9,9,-600,600,x^3-2*x^2-5*x-5)}}}
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graph of f*g(x) is graph of x^5 + 5x^4 + 7x^3 + 4x^2 + 10x + 14 shown below
{{{graph(800,800,-9,9,-50000,100000,x^5+5*x^4+7*x^3+4*x^2+10*x+14)}}}
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graph of f/g(x) is graph of (2x^2+5x+7)/(x^3+2) shown below
{{{graph(800,800,-9,9,-10,10,(2*x^2+5*x+7)/(x^3+2))}}}
it appears that the graph is good for all values of x except at {{{x = (-2)^(1/3)}}} where the value is undefined.
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as x^3 approaches -2 from the right (x^3 is greater than -2), the graph goes positive in a big way.
for example:
if you make x^3 = (-1.9999999999999), which is greater than -2, you'll see that the value of y becomes 3.86114E+13 which is a very large positive number. 
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as x^3 approaches -2 from the left (x^3 is smaller than -2), the graph goes negative in a big way.
for example:
if you make x^3 = (-2.0000000000001). which is less than -2, you'll see that the value of y becomes -3.89561E+13 which is a very large negative number.
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the graph does not appear to be able to show this as the intervals between x values appear to be too small to be captured.