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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1:20 minutes

Problem 54

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(10)

Verified step by step guidance

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

Substitute x = 10 into the function g(x).

Calculate g(10) by replacing x with 10 in the expression: g(10) = -(10)^2 + 4(10) + 1.

Simplify the expression by first calculating the square: -(10)^2.

Continue simplifying by performing the multiplication and addition: 4(10) and then add 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 value into a function to determine its output. For example, to find g(10), you replace x in the function g(x) with 10, allowing you to compute the value of the function at that point.

Polynomial Functions

Polynomial functions are 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 can be analyzed for its properties such as roots and vertex.

Simplification of Expressions

Simplification of expressions involves reducing a mathematical expression to its simplest form. This can include combining like terms, factoring, or performing arithmetic operations to make the expression easier to understand or work with, which is essential when evaluating functions.