Table of contents

0. Review of Algebra4h 18m
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 22m
10. Combinatorics & Probability1h 45m

2. Graphs of Equations

Graphs and Coordinates

College Algebra

2. Graphs of Equations

Graphs and Coordinates

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1:36 minutes

Problem 29

Textbook Question

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify.g(x) = x² + 2x + 3a. g(-1)

Verified step by step guidance

Identify the function: \( g(x) = x^2 + 2x + 3 \).

Substitute \( x = -1 \) into the function: \( g(-1) = (-1)^2 + 2(-1) + 3 \).

Calculate \((-1)^2\), which is \(1\).

Calculate \(2(-1)\), which is \(-2\).

Combine the results: \(1 - 2 + 3\).

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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 g(x) at x = -1, we replace x in the function g(x) = x² + 2x + 3 with -1, allowing us to compute the output value of the function.

Polynomial Functions

The function g(x) = x² + 2x + 3 is a polynomial function, specifically a quadratic function because its highest degree term is x². Understanding polynomial functions is essential as they are characterized by their degree, leading coefficient, and the behavior of their graphs, which can include features like vertex and axis of symmetry.

Simplification

Simplification in algebra 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 to present the final answer clearly.