i need help finding the domain and range!!!

Question

please help me find the following for the function- 4x^(6)+2x^(5)-2x^(4)+2x^(3)-0x^(2)+0x-6

1. Domain and range
2. The y-intercept
3. All real and complex zeros
4. Minimums and maximums
5. A description of the end behavior

Answer 1

I assume that this is a polynomial:

Domain: all x in Real Numbers

Range: Will need to look at end point behavior and min/max. We'll answer after we determine that information

End Point Behavior: The lead term determines the behavior as x goes to +/- infinity. The x^{^}6 term will go to + infinity in both cases, so the upper bound on P(x) is infinite.

y-intercept is easy: just constant term (x=0) y(0) = -6

zeroes: 1 works. There is another real zero and 2 sets of complex conjugates

Minimum: You can take the derivative and find the real zero at (-1,-8) with -8 being the min of y, so y ∈ [-8,∞)

Otherwise, plot the function on Desmos or use Wolfram Alpha to find roots.