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Which graphs in Exercises 29–34 represent functions that have inverse functions?
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- 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
Capitolo 3, Problema 29a
In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify.g(x) = x² + 2x + 3 a. g(-1)
Guida verificata passo dopo passo1
Substitute the given value of the independent variable, x = -1, into the function g(x) = x² + 2x + 3. This means replacing every instance of x in the function with -1.
Write the substituted expression: g(-1) = (-1)² + 2(-1) + 3.
Simplify the first term: (-1)² = 1.
Simplify the second term: 2(-1) = -2.
Combine all the terms: g(-1) = 1 - 2 + 3. Simplify further to get the final result.
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Function Evaluation
Function evaluation involves substituting a specific value for the independent variable in a function to find the corresponding output. In this case, we replace 'x' in the function g(x) = x² + 2x + 3 with -1 to determine g(-1). This process is fundamental in understanding how functions operate and how to compute their values.
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Evaluating Composed Functions
Polynomial Functions
The function g(x) = x² + 2x + 3 is a polynomial function, specifically a quadratic function because its highest degree is 2. Polynomial functions are composed of variables raised to whole number powers and can be analyzed for their behavior, roots, and graphing characteristics. Understanding the structure of polynomial functions is essential for evaluating them.
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06:04Introduction to Polynomial Functions
Simplification
Simplification refers to the process of reducing an expression to its simplest form. After evaluating the function g(-1), the resulting expression may need to be simplified by combining like terms or performing arithmetic operations. This step is crucial for presenting the final answer clearly and concisely.
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04:15Multiply Polynomials Using the Distributive Property
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