# College Algebra Video Series

Section numbers refer to Algebra and Trigonometry, Ninth Edition, by Sullivan.

All videos by James Hamblin, Shippensburg University Mathematics Department.

## Overview

This video series contains three types of videos:

• Memory Lane: These videos remind you of important concepts that you learned in your previous studies.
• Brainstorming: These videos explore new topics and contain important definitions or mathematical facts that we will be using.
• Examples: These videos contain example problems that are worked out, step by step.

Watch each video multiple times if necessary, taking notes where appropriate.

### Section 1.7: Problem Solving (Linear)

• Example: Interest Problem (Linear)
A bank loaned out $12,000, part of it at the rate of 8% per year, and the rest at the rate of 18% per year. If the interest received totaled$1000, how much was loaned at 8%?
• Example: Mixture Problem (Linear)

### Section 4.1: Linear Functions and Their Properties

• Brainstorming: Using Average Rate of Change to Identify Linear Functions
Given two different tables of values, compute ARC to determine if the functions are linear or not
• Example: Supply and Demand
Define "quantity supplied", "quantity demanded", and "equilibrium price." Suppose S(p)=-200+50p and D(p)=1000-25p. (a) Graph these equations. (b) Find the equilibrium price and equilibrium quantity. (c) Determine the prices for which the quantity demanded is higher than the quantity supplied.

### Section 1.7: Problem Solving (Quadratic)

• Example: Uniform Motion Problem
A motorboat heads upstream a distance of 24 miles on a river whose current is running at 3 miles per hour. The trip up and back takes 6 hours. Assuming that the motorboat maintained a constant speed relative to the water, what was its speed?
• Example: Another Uniform Motion Problem
A plane normally travels from City A to City B, a distance of 1200 miles, at a speed of 300 miles per hour. One day, the plane encountered a headwind, and the trip took an extra hour. What was the speed of the headwind?
• Example: "Working Together" Problem
It takes Andy 40 minutes to do a particular job alone. It takes Brenda 50 minutes to do the same job alone. How long would it take them if they worked together?
If Eli and Payton work together to clean their house, it takes them 2 hours. Working alone, Payton can do it three hours faster than Eli can. How fast can Payton clean the house?

### Section 4.4: Build Quadratic Models from Verbal Descriptions and From Data

• Example: Building a Quadratic Model
A farmer with 4000 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed?

### Section 3.4: Library of Functions

• Memory Lane: Library of Common Functions
Basic properties (domain, intercepts, symmetry) of constant function, identity function, square function, cube function, square root, cube root, reciprocal function, and absolute value

### Section 3.4: Piecewise-Defined Functions

• Brainstorming: Piecewise-defined Functions
Given f(x)=x^2 if x<2, 5 if x=2, and -2x+10 if x>2, evaluate f(-3), f(4), f(2), and graph y=f(x)
• Example: Application of Piecewise-Defined Functions

### Section 6.5: Properties of Logarithms

• Example: Using Log Properties
Discuss basic properties of logs and their exponential counterparts. Write log_2(x*sqrt(x^2+1)) as a sum of logarithms. If log_b 2 = X and log_b 3 = Y, write log_b 12 in terms of X and Y.

### Section 5.2: Properties of Rational Functions

• Brainstorming: Finding the Domain of a Rational Function
Domain is all real numbers except those that make the denominator equal zero. Find the domain of f(x) = (x^2+x-5)/(x^2-x-6). Find the domain of f(x)=(3x^3-x^2+16)/((x-3)^2(x+5)(x+1)).
• Brainstorming: What is an Asymptote?
Define vertical asymptote. Use table of values to show that f(x)=(2x)/(x-3) has a vertical asymptote at x=3. Define horizontal asymptote. Use table of values of show that f(x)=(2x)/(x-3) has a horizontal asymptote at y=2. Graph f(x)=(2x)/(x-3).