SOLUTION: Analyze the polynomial function f(x)=x^3+x^2-2x Determine the end behavior of the graph of the function. Determine the real zeros of the function and their multiplicity. Use this i

Algebra ->  Functions -> SOLUTION: Analyze the polynomial function f(x)=x^3+x^2-2x Determine the end behavior of the graph of the function. Determine the real zeros of the function and their multiplicity. Use this i      Log On


   

Question 854379: Analyze the polynomial function f(x)=x^3+x^2-2x Determine the end behavior of the graph of the function. Determine the real zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x-axis at each x-intercept. Also, determine the domain and range of function as well as the x and y intercepts. Help!! Not sure on any of this!!
Found 2 solutions by josgarithmetic, richwmiller:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Some of the answer:

Degree 3, odd degree, positive coefficient on leading term; means the function increases as x goes positive without bound, and the function decreases as x goes negative without bound.

Start with x%28x%5E2%2Bx-2%29 to look for the zeros. Three Real zeros, two of them irrational. One of the zeros is obviously at x=0.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
there are three roots
complex roots always come in pairs
There are 2 or no complex roots
There is 1 or three real roots
three real roots
0 = x (x^2+x-2)
0 = (x-1) x (x+2)
0,1,-2
the domain and range are the possible values for x and y
is there any reason to eliminate any numbers?
division by zero?
no all real numbers are the range and the domain as well

To find the x intercept set y=0 (find the roots or zeroes)
To find the y intercepts set x=0
when x=0 y=0