Ben K. answered • 12/31/15

JHU Grad specializing in Math and Science

^{2}

^{2}, the power is even. The graph of that looks like a smile with a clear bottom value for y, so it can't go to both positive and negative infinity.

Anthony M.

asked • 12/31/15 find the range and domain of this polynomial equation

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Ben K. answered • 12/31/15

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Every polynomial has a domain of (-∞,∞). The domain is the span of x values that are possible. This is easily proven by plugging in any x value. We always get some number for f(x).

The range is the extent of the possible 'y' values. For even functions (that is, the largest power of x is an even number) the range needs some farther analysis. For odd functions (the highest power of x is an odd number) the range is again (-∞,∞).

Think about the range for two functions you're probably already familiar with: f(x)=x and f(x)=x^{2}

f(x) = x is a line, and the power of x is 1, which is an odd number. It is clear that the y values go from negative infinity to positive infinity. For f(x) = x^{2}, the power is even. The graph of that looks like a smile with a clear bottom value for y, so it can't go to both positive and negative infinity.

I hope this helps!

Raphael D. answered • 12/31/15

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what are the range and domain of the function f(x)=3x^9+x^3+x^2+3x?

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The domain is obviously the set of real numbers (-inf. to +inf.)

Looking at limits of function, we see it's turning +inf. and -inf correspondingly at x approaches to +inf and -inf. (remember: at big x's function/polynomial behaves like the leading term. )

Thus, both, the domain and the range of the function would be (-inf, +inf)

P.S. at big x's function/polynomial behaves like the leading term

Michael J. answered • 01/01/16

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All polynomial functions have a domain and range in the interval (-∞, ∞). There is no limit or restriction for this type of function.

The only time you will have limitations and restrictions in the domain and range is when the function is rational, exponential, and radical. For example:

A(x) = (2x^{2} + 1) / (x^{2} + 4) ----> rational function

Q(x) = 2^{x} -------> exponential function

R(x) = √(x^{2} + 4x + 4) -----> radical function

W(x) = (2x) / √(x^{2} - 9) -----> rational function with a radical

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Ben K.

^{2}can only be positive and it has a minimum value of 0, therefore it has a range of [0,∞).01/01/16