Mathematics for Business Studies - Polynomial Functions and Derivation
Learn about the definition, graphing, equations and derivations of polynomial functions from this free online course.Publisher: ADU
CertificationView course modules
Polynomial Function and Derivation is a free online course from Alison that provides an introduction to the functionalities of polynomial functions and derivations. You will be taught the definition, degree, and classification by degree of the polynomial functions. Study the various cases used to show the domain and range of a polynomial function. You will be introduced to the basics and principles used in finding zeros of a polynomial function. The possible end behaviors of a polynomial function in addition to the method used in finding intercepts of the graph of a polynomial function will also be introduced in this course. Explore the steps needed to draw a reasonable polynomial equation graph as well as the graphing of a polynomial function by using reflections, dilations, and translations. Learn about the number of turning points as well as the creation of sign charts of the polynomial factors. Taking this course will expose learners to the approaches used in finding the equation of a Polynomial Function. The conjugate root theorems, as well as the special techniques for 2nd and 3rd-degree polynomials, will also be evaluated in this course.
This course highlights reasons why a polynomial function, P(x) of degree 'n' must have one and only one y-intercept. You will also be taught the reasons why the x-intercepts, P(x) = 0, may be anywhere from zero to "n" on a graph. This course connects to past known teachings which show that we can simply create a table of values for a function by selecting points at random, and then connect the dots. You will learn that you may or may not include the most important features of the function when attempting to plot a graph. For example, when graphing a parabola, we took the trouble to locate its axis of symmetry, which then gave us a way of getting the vertex or turning point of the parabola. Do you want to learn how to show the essential features of a graph, then this course is for you. Study the creation of a table of values with the vertex as the center. The method of locating the y-intercept of the parabola and any real zeros that might exist will be explained to you. You will learn that when one variable quantity, y, depends on another, x, the derivative will tell us the instantaneous rate of change of y with respect to x. Learn about the quantities associated with the polynomial graph which are usually distance and time, momentum and velocity, financial assets and time, air pressure and height, to name just a few examples. Study the numerous pairs of variable quantities that the derivative deals.
Lastly, If you seek to understand the derivation of polynomials, this course is best for you as the average and instantaneous rate of change will be discussed in this course. You will learn about the methods used in finding the slope of a curve at a point and the slope of the tangent to a curve. Study the concept and methods to finding the equation of the normal line of a curve at a given point in addition to one-sided derivatives. You also be taught about the definition as well as the application of a derivative and notation. You will learn about the essential concepts, important principles, and applications of Differentiability and Continuity. Finally, the appropriate concepts and illustrative used to explain the Intermediate Value Theorem will also be covered in this course. This course will be of great benefit to learners, students, researchers in business mathematics, commercial enterprises, business majors, and all who have an interest in mathematics for business studies. Register for this course today and begin your next learning journey!
Graphs of Polynomial Functions
Graphs of Polynomial Functions - Learning Outcomes
Introduction to Polynomial Functions
Finding Zeros of a Polynomial Function
Graphing Polynomial Functions
Finding the Equation of a Polynomial Function
Graphs of Polynomial Functions - Lesson Summary
The Derivative - Learning Outcomes
Rate of Change and Slope to a Curve
Normal to a Curve
Differentiability and Continuity
The Derivative - Lesson Summary
Upon the successful completion of this course, You will be able to:
- Define a Polynomial Function.
- List the types of Polynomial Functions.
- Discuss the domain and range of a Polynomial Function.
- Analyze the factoring of Polynomial Functions and finding real zeros of a Polynomial.
- Outline how to find the equation of a Polynomial from its zeros and from a graph.
- Explain how to graph polynomial functions using algebraic techniques and graphing utilities.
- Discuss how to identify other important features of polynomials such as relative extreme and end behavior.
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