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Why the graph of a polynomial function with real coefficients must have a y-intercept but may have no x-intercept?
For a polynomial of the form y = p(x) (i.e., some polynomial function of x), having a y-intercept simply means that the polynomial is defined for x = 0 - and a polynomial is defined for any value of "x". As for the x-intercept: from left to right, a polynomial of even degree may come down, not quite reach zero, and then go back up again. A simple example is y = x2 + 1.
Why is the situation for "x" and for "y" different? Well, the original equation is a polynomial in "x"; but if you solve for "x", you don't get a polynomial in "y".
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What are the Basic concepts of rational function?
Thee basic concept is that an rational function is one polynomial divided by another polynomial. The coefficients of these polynomials need not be rational numbers.
Can you have quadratic function with one real root and are complex root?
Yes, but in this case, the coefficients of the polynomial can not all be real.
What is a polynomial function?
A polynomial function of a variable, x, is a function whose terms consist of constant coefficients and non-negative integer powers of x. The general form is p(x) = a0 + a1*x + a2*x^2 + a3*x^3 + ... + an*x^n where a0, a1, ... , an are constants.
Can the exponents in a polynomial function be negative?
No. It would not be a polynomial function then.
What is the difference between a function and a polynomial?
A polynomial is specifically a function that resembles the example below: 4x5 + 3x3 - 6x2 + 7x0It consists of a variable raised to integer exponents and multiplied by different coefficients, and has multiple elements - in the above example, four. A function is a more general term to describe anything whatsoever that it done to one or more variables. For instance: arctan(4e3x)
