Aug 2510:04 PM
1.1 Introduction to Graphing 1.2 Functions and Graphs 1.3 Linear Functions, Slope, and Applications 1.4 Equations of Lines and Modeling 1.5 Linear Equations, Functions, Zeros and Applications 1.6 Solving Linear Inequalities CHAPTER 1: Graphs, Functions, and Models MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community CollegeAn equation is a statement that two expressions are equal. To solve an equation in one variable is to find all the values of the variable that make the equation true.
Each of these numbers is a solution of the equation. The set of all solutions of an equation is its solution set.
Equations and Solutions
A linear equation in one variable is an equation that can be expressed in the form mx + b = 0, where m and b are real numbers and m ≠ 0.
Equations that have the same solution set are equivalent equations.
Aug 2510:14 PM
The Addition Principle:
If
a
=
b
is true, then
a
+
c
=
b
+
c
is true.
The Multiplication Principle:
If
a
=
b
is true, then
ac
=
bc
is true.
EquationSolving Principles
Simple Interest I = Prt I = the simple interest ($) P = the principal ($) r = the interest rate (%) t = time (years) Distance FormulaThe distance d traveled by an object moving at rate r in time t is given by
d = rt.
Aug 2510:20 PM
Zeros of Linear Functions
An input
c
of a function
f
is called a
zero
of the
function, if the output for the function is 0 when the
input is
c
. That is,
c
is a zero of
f
if
f
(
c
) = 0.
A linear function
f
(
x
) =
mx + b
, with
m
≠
0,
has
exactly one zero.
A
formula
is an equation that can be used to
model
a situation.
We have used the motion formula,
d
=
r
•
t
.
We have used the simpleinterest formula,
I
=
Prt
.
We can use the equationsolving principles to solve
a formula for a given variable.
Aug 267:01 AM
134/4. Solve (6/5)y + 3 = 3/10 1.5 Linear Equations, Functions, Zeros and Applications 134/10. Solve 10x 3 = 8 + 10xAug 267:01 AM
134/22. Solve 4x + 3 = 2x 7 1.5 Linear Equations, Functions, Zeros and Applications 134/30. Solve 4(3x + 2) 7 = 3(x 2)Aug 267:01 AM
134/37. Ocean Depth. The average depth of the Pacific Ocean is 14,040 ft. This is 8890 ft less than the sum of the average depths of the Atlantic Ocean and the Indian Ocean. The average depth of the Indian Ocean is 272 ft less than fourfifths of the average depth of the Atlantic Ocean. (Source: Time Almanac, 2010) Find the average depth of the Indian Ocean.
Aug 267:01 AM
135/38. Where the Textbook Dollar Goes. Of each dollar spent on textbooks at college bookstores, 22.3 cents goes to the college store for profit, store operations, and personnel. On average, a college student at a fouryear college spends $ 667 per year for textbooks. (Source: National Association of College Stores) How much of this expenditure goes to the college store?
1.5 Linear Equations, Functions, Zeros and Applications
Aug 267:01 AM
135/40. Nutrition. A slice of carrot cake from the popular restaurant The Cheesecake Factory contains 1560 calories. This is threefourths of the average daily calorie requirement for many adults. ( Source: The Center for Science in the Public Interest) Find the average daily calorie requirement for these adults.
1.5 Linear Equations, Functions, Zeros and Applications
Aug 267:01 AM
135/46. Commission vs. Salary. Juliet has a choice between receiving an $ 1800 monthly salary from Furniture by Design or a base salary of $ 1600 and a 4% commission on the amount of furniture she sells during the month. For what amount of sales will the two choices be equal?
1.5 Linear Equations, Functions, Zeros and Applications
Aug 267:01 AM
136/52. Garden Dimensions. The children at Tiny Tots Day Care
plant a rectangular vegetable garden with a perimeter of 39 m. The length is twice the width. Find the dimensions of the garden.
1.5 Linear Equations, Functions, Zeros and Applications
Use this to graph, calculate perimeter and area of rectangle given the width and the relationship between length and width http://cfcc.edu/faculty/cmoore/RectangleL_aW.html
Aug 267:11 AM
136/56. Water Weight. Water accounts for 60% of a man's weight ( Source: ga.water.usgs.gov/edu). Jake weighs 186 lb. How much of his body weight is water?
1.5 Linear Equations, Functions, Zeros and Applications
Aug 267:12 AM
136/60. Traveling Downstream. Angelos kayak travels 14 km/hr in still water. If the rivers current flows at a rate of 2 km/hr , how long will it take him to travel 20 km downstream?
Aug 267:12 AM
136/64. Student Loans. Dimitri's two student loans total $ 9000. One loan is at 5% simple interest and the other is at 6% simple interest. At the end of 1 yr, Dimitri owes $ 492 in interest. What is the amount of each loan?
1.5 Linear Equations, Functions, Zeros and Applications
Aug 267:12 AM
137/76. Find the zero of the linear function: f(x) = 2x + 7. 1.5 Linear Equations, Functions, Zeros and Applications
Solve algebraically and graphically.
137/82. Find the zero of the linear function: f(x) = 3x + 13. Solve algebraically and graphically.
Aug 267:12 AM
1.5 Linear Equations, Functions, Zeros and Applications
137/82. Find the zero of the linear function: f(x) = 3x + 13.
Solve algebraically and graphically.
137/76. Find the zero of the linear function: f(x) = 2x + 7.
Solve algebraically and graphically.
Aug 267:12 AM
In Exercises 8792, use the given graph to find each of the following: (a) the x intercept and (b) the zero of the function.
138/90.
1.5 Linear Equations, Functions, Zeros and Applications
Jan 179:02 AM
Aug 267:12 AM
In Exercises 8792, use the given graph to find each of the following: (a) the x intercept and (b) the zero of the function. 138/90.
1.5 Linear Equations, Functions, Zeros and Applications
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Aug 267:12 AM
In Exercises 8792, use the given graph to find each of the following: (a) the x intercept and (b) the zero of the function. 138/92.
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Aug 267:12 AM
In Exercises 8792, use the given graph to find each of the following: (a) the x intercept and (b) the zero of the function. 138/92.
1.5 Linear Equations, Functions, Zeros and Applications
