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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".
What else can I help you with?
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)
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 are all of the zeros of this polynomial function f(a)=a^4-81?
Find All Possible Roots/Zeros Using the Rational Roots Test f(x)=x^4-81 ... If a polynomial function has integer coefficients, then every rational zero will ...
If you are asked to write a polynomial function of least degree with real coefficients and with zeros of 2 and i square roots of seven what would be the degree of the polynomial also wright equation?
3y2-5xyz yay i figured it out!!!!
How do you write a polynomial function with rational coefficients in standard form with given zeros of -1 -1 1?
The polynomial is (x + 1)*(x + 1)*(x - 1) = x3 + x2 - x - 1
Which polynomial has rational coefficients a leading leading coefficient of 1 and the zeros at 2-3i and 4?
There cannot be such a polynomial. If a polynomial has rational coefficients, then any complex roots must come in conjugate pairs. In this case the conjugate for 2-3i is not a root. Consequently, either (a) the function is not a polynomial, or (b) it does not have rational coefficients, or (c) 2 - 3i is not a root (nor any other complex number), or (d) there are other roots that have not been mentioned. In the last case, the polynomial could have any number of additional (unlisted) roots and is therefore indeterminate.
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.
What do you mean by a function identically equal to zero?
A polynomial is identically equal to zero if and only if all of its coefficients are equal to zero. eg. The power series on the left is identically equal to zero, consequently all of its coefficients are equal to 0:
Can the exponents in a polynomial function be negative?
No. It would not be a polynomial function then.
Why the graph of a polynomial function with real coefficients must have a y intercept but no x intercept?
A polynomial function is defined for all x, ranging from minus infinity to plus infinity. Since it is defined for all x, it is defined for x = 0 and this is the point where it intersects the y-axis which is called the y-intercept. It is possible, with suitable choice of coefficients that the function is always positive or always negative. In either case it will not cross the x-axis so that there is no x-intercept. However, it is not true to say that all polynomial functions with real coefficients do not have an x-intercept. In fact all polynomials of odd order (linear, cubic, quintic etc) will have at least one x-intercept.
A polynomial function is always continuous?
Yes, a polynomial function is always continuous
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)
