Intermediate Algebra

Lisa Healey

Description

• Solutions to Odd-Numbered Problems

Intermediate Algebra provides precollege algebra students with the essentials for understanding what algebra is, how it works, and why it so useful. It is written with plain language and includes annotated examples and practice exercises so that even students with an aversion to math will understand these ideas and learn how to apply them. This textbook expands on algebraic concepts that students need to progress with mathematics at the college level, including linear, exponential, logarithmic, and quadratic functions; sequences; and dimensional analysis. Written by faculty at Chemeketa Community College for the students in the classroom, Intermediate Algebra is a classroom-tested textbook that sets students up for success.

• Chapter 1: Graphs and Linear Functions
• Chapter 2: Exponential Functions
• Chapter 3: Logarithmic Functions
• Chapter 4: Quadratic Functions
• Chapter 5: Further Topics in Algebra
• Glossary
• Index

Sujets

• Sciences et techniques
• Álgebra
• Algebra
• Intermediate
• Mathematics
• Abrégé du calcul par la restauration et la comparaison

Informations

• Publié par: Chemeketa Press
• Date de parution: 28 avril 2021
• Nombre de lectures: 0
• EAN13: 9781943536900
• Langue: English
• Poids de l'ouvrage: 6 Mo

Extrait

Intermediate Algebra
by Lisa Healey
Intermediate Algebra
ISBN: 978-1-943536-30-6
Edition 1.2 Fall 2018
2018, Chemeketa Community College. All rights reserved.
Chemeketa Press
Chemeketa Press is a nonprofit publishing endeavor at Chemeketa Community College. Working together with faculty, staff, and students, we develop and publish affordable and effective alternatives to commercial textbooks. All proceeds from the sale of this book will be used to develop new textbooks. For more information, please visit chemeketapress.org .
Publisher: Tim Rogers
Managing Editor: Steve Richardson
Production Editor: Brian Mosher
Manuscript Editors: Steve Richardson, Matt Schmidgall
Design Editor: Ronald Cox IV
Cover Design: Ronald Cox IV
Interior Design: Ronald Cox IV, Kristi Etzel, Kristen MacDonald
Layout: Noah Barrera, Matthew Sanchez, Faith Martinmaas, Emily Evans, Shaun Jaquez, Steve Richardson, Kristi Etzel, Cierra Maher, Candace Johnson
Additional contributions to the design and publication of this textbook come from the students and faculty in the Visual Communications program at Chemeketa.
Chemeketa Math Faculty
The development of this text and its accompanying MyOpenMath classroom has benefited from the contributions of many Chemeketa math faculty in addition to the author, including:
Ken Anderson, Benjamin Gort, Kyle Katsinis, Tim Merzenich, Nolan Mitchell, Martin Prather, Keith Schloeman, Rick Rieman, and Toby Wagner
Text Acknowledgment
This book was originally developed using materials from OpenStax College Algebra , by OpenStax College, which have been made available under a Creative Commons Attribution 4.0 license and may be downloaded for free from cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d .
Printed in the United States of America.
Contents
Chapter 1: Graphs and Linear Functions
1.1 Qualitative Graphs
1.2 Functions
1.3 Finding Equations of Linear Functions
1.4 Using Linear Functions to Model Data
1.5 Function Notation and Making Predictions
Chapter 2: Exponential Functions
2.1 Properties of Exponents
2.2 Rational Exponents
2.3 Exponential Functions
2.4 Finding Equations of Exponential Functions
2.5 Using Exponential Functions to Model Data
Chapter 3: Logarithmic Functions
3.1 Introduction to Logarithmic Functions
3.2 Properties of Logarithms
3.3 Natural Logarithms
Chapter 4: Quadratic Functions
4.1 Expanding and Factoring Polynomials
4.2 Quadratic Functions in Standard Form
4.3 The Square Root Property
4.4 The Quadratic Formula
4.5 Modeling with Quadratic Functions
Chapter 5: Further Topics in Algebra
5.1 Variation
5.2 Arithmetic Sequences
5.3 Geometric Sequences
5.4 Dimensional Analysis
Solutions to Odd-Numbered Exercises
Glossary/Index
CHAPTER 1
Graphs and Linear Functions
Toward the end of the twentieth century, the values of stocks of Internet and technology companies rose dramatically. As a result, the Standard and Poor s stock market average rose as well.
Figure 1 tracks the value of an initial investment of just under $100 over 40 years. It shows an investment that was worth less than $500 until about 1995 skyrocketed up to almost $1500 by the beginning of 2000. That five-year period became known as the dot-com bubble because so many Internet startups were formed. The dot-com bubble eventually burst. Many companies grew too fast and then suddenly went out of business. The result caused the sharp decline represented on the graph beginning around the year 2000.

Figure 1.
Notice, as we consider this example, there is a relationship between the year and stock market average. For any year, we choose we can estimate the corresponding value of the stock market average. Analyzing this graph allows us to observe the relationship between the stock market average and years in the past.
In this chapter, we will explore the nature of the relationship between two quantities.
1.1 Qualitative Graphs
1.2 Functions
1.3 Finding Equations of Linear Functions
1.4 Using Linear Functions to Model Data
1.5 Function Notation and Making Predictions

1.1 Qualitative Graphs
Overview
In this section, we will see that, even without using numbers, a graph is a mathematical tool that can describe a wide variety of relationships. For example, there is a relationship between outdoor temperatures over the course of a year and the retail sales of ice cream. We can describe this relationship in a general way using a qualitative graph. As you study this section, you will learn to:
Read and interpret qualitative graphs
Identify independent and dependent variables
Identify and interpret an intercept of a graph
Identify increasing and decreasing curves
Sketch qualitative graphs
A. Reading a Qualitative Graph
Both qualitative and quantitative graphs can have two axes and show the relationship between two variables. We also read both types of graph from left to right - just like a sentence. The difference is that quantitative graphs have numerical increments on the axes (scaling and tick marks), while qualitative graphs only illustrate the general relationship between two variables.

Example 1
Use the qualitative graph, Figure 1 , and the quantitative graph, Figure 2 , to answer the following questions.

Figure 1. The sale of ice cream at Joe s Caf (a qualitative graph).

Figure 2. The population of Portland, Oregon (a quantitative graph).
1. What does the qualitative graph tell us about ice cream sales at Joe s Caf ? Do we know how many servings were sold in June?
2. What does the quantitative graph tell us about the population of Portland, Oregon? What was the population in 1930?
Solutions
1. Ice cream sales are lowest at the beginning and at the end of the year and highest during the middle months. We cannot tell from this graph exactly how many servings are sold in any given month.
2. The population of Portland, Oregon, has been increasing since 1850, except for a slight decrease in the 1950s and 1970s. The population in 1930 was about 300,000.
B. Independent and Dependent Variables
A qualitative graph is a visual description of the relationship between two variables. The graph tells a story about how one quantity is determined or influenced by another quantity. For example, the number of calories one consumes in a week determines the number of pounds one will lose (or gain) that week. Another way to say this is that the change in a person s weight is dependent on the number of calories they consume.
We can assign variables to the quantities in the relationship between calories consumed and weight. Let c be the number of calories consumed in a week and let w be the weight change in pounds of the person who is counting calories. In this example, the quantity of weight change depends on the number of calories consumed, so we call w the dependent variable . Because the number of calories consumed determines or influences the weight change, we call c the independent variable.
When creating a qualitative graph that depicts the relationship between two variables, the first step is to determine which of the variables is independent and which is dependent. Let s say we want to depict the relationship between p , the number of bushels of potatoes produced on an acre of farmland, and k , the number of kilograms of fertilizer applied to the acre. We can phrase the relationship two different ways and determine which makes the most sense.
We can say, The yield of potatoes depends on the amount of fertilizer, or, The amount of fertilizer depends on the yield of potatoes. It makes more sense to say that p , the bushels of potatoes yielded, depends on k , the amount of fertilizer used, so p is the dependent variable. The amount of fertilizer used, k , is the independent variable because it influences the number of bushels produced.
Independent and Dependent Variables

In the relationship between two variables, p and t , if p depends on t , then we call p the dependent variable and t the.

Example 2
Identify the independent variable and the dependent variable for each situation.
1. Let p represent the average price of a home in Salem, Oregon, and let t represent the number of years since 1990.
2. Let r represent the rate in gallons per minute that water is added to a bathtub, and let m be the number of minutes it takes to fill the tub.
Solutions
1. We say that the price p depends on or is determined by the year t . It is therefore the dependent variable. We would not say the year t depends on the average price of a home p . Time is independent of the price. Whether the average price goes up or down, time keeps passing into the future. So we call t the independent variable.
2. The rate of water flow determines how quickly the tub fills, so r is the independent variable. The number of minutes it takes to fill the tub depends on this rate, so m is the dependent variable.
Practice B

Determine the independent variable and the dependent variable for each situation. Turn the page to check your solutions.
1. Let m be the number of minutes since a cup of hot tea was poured, and let T be the temperature of the tea.
2. Let g be a student s exam score, and let s be the amount of time the student spent studying for the exam.
3. Let F be the outside temperature, and let c be the number of winter coats that a department store sells.
4. Let v be the resale v