Table of contents

0. Review of Algebra4h 18m

Algebraic Expressions
36m

Exponents
32m

Polynomials Intro
19m

Multiplying Polynomials
36m

Factoring Polynomials
1h 2m

Radical Expressions
15m

Simplifying Radical Expressions
35m

Rationalize Denominator
15m

Rational Exponents
4m

1. Equations & Inequalities3h 18m

Linear Equations
31m

Rational Equations
21m

The Imaginary Unit
6m

Powers of i
11m

Complex Numbers
36m

Intro to Quadratic Equations
18m

The Square Root Property
11m

Completing the Square
12m

The Quadratic Formula
18m

Choosing a Method to Solve Quadratics
9m

Linear Inequalities
20m

2. Graphs of Equations1h 43m

Graphs and Coordinates
7m

Two-Variable Equations
23m

Lines
1h 12m

3. Functions2h 17m

Intro to Functions & Their Graphs
35m

Common Functions
5m

Transformations
45m

Function Operations
21m

Function Composition
29m

4. Polynomial Functions1h 44m

Quadratic Functions
39m

Understanding Polynomial Functions
34m

Graphing Polynomial Functions
30m

Dividing Polynomials

Zeros of Polynomial Functions

5. Rational Functions1h 23m

Introduction to Rational Functions
9m

Asymptotes
35m

Graphing Rational Functions
38m

6. Exponential & Logarithmic Functions2h 28m

Introduction to Exponential Functions
9m

Graphing Exponential Functions
25m

The Number e
8m

Introduction to Logarithms
22m

Graphing Logarithmic Functions
18m

Properties of Logarithms
27m

Solving Exponential and Logarithmic Equations
35m

7. Systems of Equations & Matrices4h 5m

Two Variable Systems of Linear Equations
1h 7m

Introduction to Matrices
1h 11m

Determinants and Cramer's Rule
1h 3m

Graphing Systems of Inequalities
42m

8. Conic Sections2h 23m

Introduction to Conic Sections
5m

Circles
15m

Ellipses: Standard Form
33m

Parabolas
36m

Hyperbolas at the Origin
40m

Hyperbolas NOT at the Origin
12m

9. Sequences, Series, & Induction1h 22m

Sequences
40m

Arithmetic Sequences
25m

Geometric Sequences
15m

10. Combinatorics & Probability1h 45m

Factorials
11m

Combinatorics
46m

Probability
47m

2. Graphs of Equations

Graphs and Coordinates

College Algebra

2. Graphs of Equations

Graphs and Coordinates

Previous problemNext problem

1:16 minutes

Problem 38b

Textbook Question

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(x) = |x+3|/|x + 3| b. f(-5)

Verified step by step guidance

Step 1: Understand the function f(x) = |x + 3| / |x + 3|. This function involves absolute values in both the numerator and denominator. The absolute value of a number is its distance from zero, so it is always non-negative.

Step 2: Substitute the given value of x = -5 into the function. This means replacing x with -5 in both the numerator and denominator: f(-5) = |(-5) + 3| / |(-5) + 3|.

Step 3: Simplify the expressions inside the absolute value bars. For the numerator and denominator, calculate (-5) + 3, which equals -2. So the function becomes f(-5) = |-2| / |-2|.

Step 4: Evaluate the absolute values. The absolute value of -2 is 2, so the function simplifies to f(-5) = 2 / 2.

Step 5: Simplify the fraction. Divide the numerator by the denominator to find the simplified value of the function at x = -5.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

0 Comments

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Absolute Value Function

The absolute value function, denoted as |x|, represents the distance of a number x from zero on the number line, always yielding a non-negative result. For example, |3| = 3 and |-3| = 3. This function is crucial in evaluating expressions that involve both positive and negative values, as it affects the outcome based on the sign of the input.

Evaluating Functions

Evaluating a function involves substituting a specific value for the independent variable (in this case, x) into the function's expression. This process allows us to determine the corresponding output value. For instance, to evaluate f(-5), we replace x with -5 in the function f(x) = |x + 3| / |x + 3| and simplify the expression accordingly.

Simplifying Expressions

Simplifying expressions involves reducing them to their most basic form, often by performing arithmetic operations and applying algebraic rules. In the context of the given function, simplification may include canceling common factors or reducing fractions. Understanding how to simplify is essential for accurately determining the value of the function after evaluation.