0
What else can I help you with?
Can the leading coefficient of a polynomial function be a fraction?
Yes, the leading coefficient of a polynomial function can be a fraction. A polynomial is defined as a sum of terms, each consisting of a coefficient (which can be any real number, including fractions) multiplied by a variable raised to a non-negative integer power. Thus, the leading coefficient, which is the coefficient of the term with the highest degree, can indeed be a fraction.
What is a polynomial function f of least degree that has rational coefficient a leading coefficient of 1 and the given zeros -7 -4?
A polynomial function of least degree with rational coefficients and a leading coefficient of 1 that has the zeros -7 and -4 can be constructed using the fact that if ( r ) is a zero, then ( (x - r) ) is a factor. Therefore, the polynomial can be expressed as ( f(x) = (x + 7)(x + 4) ). Expanding this, we get ( f(x) = x^2 + 11x + 28 ). Thus, the polynomial function is ( f(x) = x^2 + 11x + 28 ).
What is the leading term in a polynomial?
The leading term in a polynomial is the term with the highest degree, which determines the polynomial's end behavior and its classification (e.g., linear, quadratic, cubic). It is typically expressed in the form ( ax^n ), where ( a ) is a non-zero coefficient and ( n ) is a non-negative integer. The leading term is crucial for understanding the polynomial's growth as the input values become very large or very small.
All polynomials have at least one maximum?
Not quite. The point at infinity cannot be regarded as a maximum since the value will continue to increase asymptotically. As a result no polynomial of odd degree can have a maximum. Only polynomials of an even degree whose leading coefficient is negative will have a global maximum.
What is the leading coefficient of each fungtion?
what is the leading coefficient -3x+8
What is a possible leading coefficient and degree for a polynomial starting in quadrant 3 and ending in quadrant 4?
Leading coefficient: Negative. Order: Any even integer.
What is the leading coefficient in a polynomial?
It is the number (coefficient) that belongs to the variable of the highest degree in a polynomial.
The rational roots of a polynomial function F(x) can be written in the form where p is a factor of the constant term of the polynomial and q is a factor of the leading coefficient.?
TRue
Where p is a factor of the leading coefficient of the polynomial and q is a factor of the constant term.?
Anywhere. Provided it is not zero, and number p can be the leading coefficient of a polynomial. And any number q can be the constant term.
What is the number in front of the term with the highest degree in a polynomial?
It is the Coefficient. It only refers to the given term that it is front. e.g. 2x^2 - 3x + 1 The '2' in front of 'x^2' only refers to 'x^2'. The '-3' in front of 'x' is the coefficient of '-3' The '1' is a constant.
When an odd function has a negative leading coefficient what happens to the graph?
the left end of the graph is going in a positive direction and the right end is going in a negative direction.
What is the rational zero theorem?
If a polynomial function, written in descending order, has integer coefficients, then any rational zero must be of the form ± p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
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.
How do I determine if a function is a power function Power functions must be able to be written as such kxa. Would I compare the function to the format of a power function For ex KEv12kv5?
Identify the degree and leading coefficient of polynomial functions. ... the bird problem, we need to understand a specific type of function. A power ... A power function is a function that can be represented in the form ... Example 3.4.1: Identifying Power Functions ... Comparing Smooth and Continuous Graphs.
The leading coefficient of a cubic polynomial p is 2 and the coefficient of the linear term is 5 and if P 0 equals 7 and P 2 equals 21 what is P 3?
N i g g e r s
All polynomials have at least one maximum?
Not quite. The point at infinity cannot be regarded as a maximum since the value will continue to increase asymptotically. As a result no polynomial of odd degree can have a maximum. Only polynomials of an even degree whose leading coefficient is negative will have a global maximum.
What are the characteristics of the function f(x)=-(x+4)^5?
)the answer is the left end of the graph of the function goes up and the right goes down, 2)it has 5 zeros and at most 4 relative maximums and minimums, 3)and it is a reflection and a translation to the left of the parent function.
