TOPICS – CHAPTER 0
Math 160 – Section 0.1 – Functions and their Graphs
Read all examples
Do problems 1-59 EOO (every other odd), practice problems and technology exercises
1) Be able to express any one of the following forms into the others
- Interval notation
- Graph
- Inequality
2) Functions:
a. Definition
b. Notation
c. Graphs of Functions: Vertical line test
d. Evaluation
i. At numbers f(#)
ii. At expressions
f(expression)
iii. At x+h
f(x+h)
e. Domain
i. Polynomial function
ii. Radical function
iii. Rational function
iv. Any combination of functions
f. Range
3) Graph interpretation. Finding any of the following:
a. F(#)
b. Is f(#) positive or negative
c. Solve f(x) = #
d. Find the zeros of the function
e. Solve inequalities (Ex. Solve f(x) ≥ 0)
f. Find x so that f(x) is maximum, minimum
g. Where is the function increasing, decreasing, constant
4) Evaluating piecewise defined functions
Math 160 – Section 0.2 – Some Important Functions
Read all examples
Do problems 1-20 odd, practice problems and technology exercises
1) Linear functions (read through example 4)
a. Graphs
b. Find x- and y- intercepts
2) Explore cost functions (read example 2, and do problem 15)
a. Graph
b. Solve problems of the type
i. Given x, find y
ii. Given y, find x
3) Rational function: The cost-benefit model (read example 5 and do problems 19 and 20)
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TOPICS – CHAPTER 0 (continued)
Math 160 – Section 0.3 – The Algebra of Functions (do 1-20 odd)
Read all examples
Do problems 1-9 odd, 13-35 odd, practice problems and technology exercises
1) Operations with functions
a. Addition
b. Subtraction (Profit function)
c. Multiplication
d. Division
e. Composition
2) Finding the difference quotient
Math 160 – Section 0.4 – Zeros of Functions – The Quadratic Formula and Factoring
Read all examples
Do problems 1-37 EOO, 39, 40, practice problems and technology exercises
1) Zeros of a function
2) Factoring quadratic polynomials
3) Using the quadratic formula
4) Write the profit equation and find the break even point (read example 4 and do problem
39)
Math 160 – Section 0.5 – Exponents and Power Functions
Read all examples
Do problems 1-70 (pick a few), 77-83 all, 85, 89, 93, 95, practice problems and technology
exercises
1) Evaluating powers of numbers
a. By hand
b. With the calculator
2) Evaluate by using laws of exponents
3) Use law of exponents to simplify
4) Compound interest
5) Change
a. From exponential to radical form
b. From radical to exponential form
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TOPICS – CHAPTER 0 (continued)
Math 160 – Section 0.6 – Functions and Graphs in Applications
Read all examples
Do problems 1-53 odd, practice problems and technology exercises
1) Writing expressions for area and perimeter of some geometric figures
2) Writing expressions for surface area and volume of some solids
3) Amount of fence functions
4) Cost of an open/closed box functions
5) Cost, revenue and profit functions. Break even point
6) Reading and interpreting graphs within context
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