what is the range of 3+15x-x^3-2x^4?

Question

studying for pre-calc final don't understand this stuff!!!!!! more questions to come

Answer 1

To find the range of that function, first note that the function is continuous, so that its sufficient to find the minimum value and the maximum value of that function, and then the range is simply (min, max).
Since lim x->inf of f(x) = -inf, then this function has no minimum value. To find the max value, solve f'(x*) = 0 and calculate f(x*). You can confirm that this is the maximum value of f(x) by show that f"(x*)<0.
The range is thus (-inf, f(x*)).

Answer 2

The range would be the set of all possible outputs or y values.
(the domain is the set of all possible input or x values)
Since the lead term is a fourth power with a negative coefficient it seems that the domain would be from a certain maximum value to negative infinity.
A graph of this equation seems to confirm this.
In general, polynomial functions have as their domain all real numbers and as their range all real numbers for odd degreed functions and from a certain point (min or max) to infinity (positive or negative infinity) for even degreed functions. This function, with its higest degree 4, is an even degreed function.
You say you're in pre-calc?
To find that maximum value, without calculus, you'd have to find the x intercepts and find a point between the x intercepts where it achieves the maximum value.
To find the x intercepts you'd set the function equal to 0 and solve, if possible, or you'd pull out your trusty graphics calculator and zoom in. You could find the max value graphically this way, also.
When you get into calculus you'll learn better ways to find this maximum value.