Explain why odd-degree polynomial functions can have only local maximums and minimums, but even-degree polynomial functions can have absolute maximums and minimums.

Q: Create 3rd degree polynomial function whose graph crosses the x-axis more than one

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Q: Analyze the polynomial function f(x)=6x(x^2-9)(x+5) The graph of f behaves like y__? for large…

A: Consider the given function.

Q: Consider the polynomial function y = 2(x - 2)³ + 5 when investigating and analyzing. Mat domain…

A: Since you have asked multiple part question, we will solve the first 3 question for you as per our…

Q: sketch the graph of the polynomial function make sure your graph shows all intercepts and exhibits…

A:

Q: A rectangle has a length of 12 units and a width of 5 units. Squares of `x` by `x` units are cut out…

A: Solution : We have given a rectangle withe length of 12 units and width of 5 units. If squares of x…

Q: Which of these best exemplifies a sketch of the graph of the polynomial function fx)=x(x-3)(x+2)?

A: A root is a value for which a given function equals zero. When that function is plotted on a graph,…

Q: What is the least possible degree of the polynomial graphed above?

A: We can use the concept of function in order to solve the given problem.

Q: A polynomial function is written in ________ form when its terms are written in descending order of…

A: Polynomial Function: A polynomial function is defined as an equation/expression consisting of…

Q: 11. Explain why odd-degree polynomial functions can have only local maximums and minimums, but even…

A: Solutions

Q: Find the upper and the lower bound of the zeroes of each polynomial function. Given Upper bound…

A: As per our guidelines we are supposed to solve only three sub part of the problem. For the solution…

Q: In Problem,construct a polynomial function f with the given characteristics.

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Q: What is the relative maximum and the relative minimum for this polynomial?

A: Given that: f(x)=11x7+17x5+2x2-0x9+0x+3

Q: True or false: Odd-degree polynomial functions have graphs with opposite behavior at each end.

A: Let us consider the odd degree polynomial y = x3. The graph is:

Q: What is a polynomialfunction in degree 1

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Q: Is it possible for a polynomial to have two local maxima and no local minimum? Explain.

A: Maxima and minima: Functions make hills and valleys when they reach a minimum or maximum value in…

Q: What is a polynomial function?

A: To Explain: what is a polynomial function

Q: Why is a third-degree polynomial function with a negative leading coefficient not appropriate for…

A: Note that a third-degree polynomial with a negative leading coefficient that used to model real-life…

Q: construct a polynomial function f with the given characteristics.     Zeros: - 4, - 1, 2; degree 3;…

A: zeroes of the polynomial are -4,-1,2 which means (x+4)(x+1)(x-2)are the factors of required…

Q: What is a local maximum point or local minimum point of a polynomial P?

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Q: What is a polynomial? What is the domain of every polynomial function?

A: given,       to define polynomial and domain of every polynomial function

Q: If a polynomial function has zeros at -2, 0, and 2, does its graph have y-axis symmetry, origin…

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Q: What is the smallest-degree polynomial that has at least one maximum and one minimum?

A: Consider a polynomial of degree 3. Consider that the derivative of a third degree polynomial is a…

Q: The graph of a polynomial function is ________, which means that the graph has no breaks,holes, or…

A: A polynomial refers to any expression that consists of variables and coefficients, that involves the…

Q: The behavior of the graph of a polynomial function to the far left or the far right is called…

A: Consider the polynomial function fx=anxn+an-1xn-1+…+a1x+a0    an≠0 In it an is called the leading…

Q: Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits…

A: P(x) = −(2x − 1)(x + 1)(x + 4)

Q: Explain how to use the Leading Coefficient Test to determine the end behavior of a polynomial…

A: case (1) When n is odd and an  is positive. Then the graph is falls to the left and rises to the…

Q: The graph of a polynomial function is given. What is the smallest degree that the polynomial could…

A: For any polynomial function of degree 'n' The smallest degree of the polynomial depends on the…

Q: 20. Explain how instantaneous rates of change could be used to locate the local maxima and local…

A: Given

Q: In Problem,tell the maximum number of real zeros that each polynomial function may have.Do not…

A: Given function is: f(x) = x6-1 We have to find the number of real zeroes of the above polynomial.

Q: Make a conjecture about the minimum and maximum number of x-intercepts possible for a polynomial…

A: Given Data: To make a conjecture about the minimum and maximum number of x- intercepts possible for…

Q: Write a polynomial function with minimum degree andleading coefficient 1 that has zeros x =…

A: If  zero is a and its multiplicity is m, we can write it as (x-a)m

Q: snip

A: f(x)=x2(x-4)(x+1)

Q: Sketch a graph of the polynomial function. Locate and label all intercepts. y =-2(x-1)* (x+2)(x-4)

A: Sketch a graph of the polynomial function.Locate and label all intercepts.      y=-2x-12x+2x-4

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: Given- If the graph of a polynomial function has three x-intercepts, then it must have at least two…

Q: What is meant by the end behavior of a polynomial function? Explain.

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Q: In Problem, form a polynomial function whose real zeros and degree are given.Answers will vary…

A: The equation of three-degree polynomial also called cubic polynomial is in the form of…

Q: P(x) = -(x – 3)²(x + 1)²

A:

Q: A rectangle has a length of 18 units and a width of 14 units. Squares of x by x units are cut out of…

A:

Q: 8. Determine algebraically the polynomial function that passes through the points below.

A: Given,

Q: Explain why odd-degree polynomials can have only local maximums and/or minimums, but even-degree…

A: The odd degree function extends its value from negative infinity to positive infinity or vice-versa…

Q: P(x) 3 x³ (x + 2)(x – 3)²

A: Given polynomial function Px=x3x+2x-32. The main objective is to sketch the graph of this polynomial…

Q: Given a polynomial function of degree 6, explain how many minimum or maximum values and how many…

A:

Q: How can a polynomial function be graphed without the use of a calculator?

A: Polynomial function can be graphed without the use of a calculater with the steps provided in next…

Q: Sketch a graph of any cubic polynomial functionthat has a negative leading coefficient and…

A: Consider a cubic polynomial P(x)=-2x3+3x2+11x-6 . This polynomial can be written in factored form as…

Q: onstruct a polynomial function with the following properties: fifth degree, 4 is a zero of…

A:

Q: What are the maximum numbers of relative extrema and points of inflection that a fifth-degree…

A: A fifth degree polynomial is to be first differentiated first.  Now the first differentiable will be…

Q: If f is a polynomial function, and f(a) and f(b) have opposite signs, what must occur between a and…

A: If we consider geometric interpretation of f, then it be more easier. (I)   As f(a) and f(b) have…

Q: Explain the similarities and differences between quadratic functions and cubic polynomial functions…

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Q: What is the equation of this degree 6 polynomial function?

A: