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

3. Functions

Intro to Functions & Their Graphs

College Algebra

3. Functions

Intro to Functions & Their Graphs

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1:33 minutes

Problem 53

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. g(-2)

Verified step by step guidance

Identify the function g(x) which is given as g(x) = -x^2 + 4x + 1.

Substitute x = -2 into the function g(x).

Calculate (-2)^2 to find the square of -2.

Substitute the value of (-2)^2 into the expression -x^2, resulting in -(-2)^2.

Simplify the expression by performing the arithmetic operations: -(-2)^2 + 4(-2) + 1.

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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 input value into a function to determine its output. For example, to find g(-2), you replace x in the function g(x) with -2, allowing you to calculate the corresponding output value. This process is fundamental in understanding how functions behave at different points.

Polynomial Functions

Polynomial functions are mathematical expressions that involve variables raised to whole number powers, combined using addition, subtraction, and multiplication. In this case, g(x) = -x^2 + 4x + 1 is a quadratic polynomial, which has a degree of 2. Understanding the structure of polynomial functions is essential for evaluating them and analyzing their properties.

Simplification of Expressions

Simplification of expressions involves reducing mathematical expressions to their simplest form, making them easier to work with. This can include combining like terms, factoring, or reducing fractions. In the context of evaluating g(-2), simplifying the resulting expression helps clarify the final output and ensures accuracy in calculations.