Textbook Question
Write the standard form of the equation of the circle with the given center and radius. Center (0, 0), r = 7
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 3, Problem 31b
Evaluate each function at the given values of the independent variable and simplify. h(x) = x4 - x2 +1 b. h (-1)
Verified step by step guidance1
Step 1: Start by substituting the given value of the independent variable, x = -1, into the function h(x). The function is h(x) = x⁴ - x² + 1. Replace every occurrence of x with -1.
Step 2: Write the substituted expression: h(-1) = (-1)⁴ - (-1)² + 1.
Step 3: Simplify each term in the expression. Recall that (-1)⁴ means multiplying -1 by itself four times, and (-1)² means multiplying -1 by itself two times.
Step 4: Combine the simplified terms to get the final expression for h(-1).
Step 5: Verify that all calculations are simplified correctly and ensure the expression is fully reduced.
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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, we replace 'x' in the function h(x) = x^4 - x² + 1 with -1. This process allows us to compute the output of the function for that particular input.
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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 the highest power of x present in the expression. Understanding polynomial functions is essential for evaluating and simplifying them.
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Simplification of Expressions
Simplification of expressions involves reducing a mathematical expression to its simplest form. After evaluating the function h(-1), we will combine like terms and perform arithmetic operations to arrive at a single numerical value. This step is crucial for providing a clear and concise answer to the evaluation of the function.
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Related Practice
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Textbook Question
In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. h(x) = x4 - x2+1 c. h (-x)
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