Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
4. Polynomial Functions
Graphing Polynomial Functions
2:41 minutes
Problem 8
Textbook Question
Textbook QuestionIn Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=x^1/3 −4x^2+7
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2mPlay a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Polynomial Functions
A polynomial function is a mathematical expression that involves variables raised to non-negative integer powers, combined using addition, subtraction, and multiplication. The general form is f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n are coefficients and n is a non-negative integer. Functions that include fractional or negative exponents do not qualify as polynomial functions.
Recommended video:
06:04
Introduction to Polynomial Functions
Degree of a Polynomial
The degree of a polynomial is the highest power of the variable in the polynomial expression. It provides insight into the polynomial's behavior, such as the number of roots and the end behavior of the graph. For example, in the polynomial f(x) = 3x^4 + 2x^2 - 5, the degree is 4, indicating that the highest exponent is 4.
Recommended video:
Guided course
05:16
Standard Form of Polynomials
Identifying Non-Polynomial Terms
To determine if a function is a polynomial, one must identify any terms that do not conform to the polynomial structure. For instance, terms with variables raised to fractional powers, like x^(1/3), or negative powers, such as x^(-2), disqualify the function from being a polynomial. Recognizing these terms is essential for accurately classifying the function.
Recommended video:
05:01
Identifying Intervals of Unknown Behavior
Watch next
Master Identifying Intervals of Unknown Behavior with a bite sized video explanation from Callie
Start learningRelated Videos
Related Practice
Textbook Question
Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing. See Example 1. ƒ(x)=2x^4
221
views
Graphing Polynomial Functions practice set
- Problem sets built by lead tutorsExpert video explanations