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
2. Graphs of Equations
Two-Variable Equations
1:51 minutes
Problem 31c
Textbook Question
Textbook QuestionIn Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. h(x) = x^4 - x²+1 c. h (-x)
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Function Evaluation
Function evaluation involves substituting a specific value for the independent variable in a function. In this case, to evaluate h(-x), we replace every instance of x in the function h(x) with -x. This process allows us to analyze how the function behaves with different inputs, which is essential for understanding its properties.
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Polynomial Functions
A polynomial function is a mathematical expression that involves variables raised to whole number powers, combined using addition, subtraction, and multiplication. The function h(x) = x^4 - x² + 1 is a polynomial of degree 4, which indicates its highest exponent. Understanding polynomial functions is crucial for evaluating and simplifying expressions, as they exhibit specific behaviors such as continuity and differentiability.
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Simplification of Expressions
Simplification of expressions involves reducing a mathematical expression to its simplest form. This can include combining like terms, factoring, or applying algebraic identities. After evaluating h(-x), simplifying the resulting expression helps in clearly understanding the function's characteristics and making further calculations or comparisons easier.
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