# Departmental Syllabus for College Algebra

**Text:** Algebra and Trigonometry custom edition for
FIU (or 8^{th} edition) by Michael Sullivan

**Description:** The focus of this course is on functions and their properties. In
particular, properties

and graphs of linear , quadratic, rational, exponential and logarithmic functions
are discussed. Ways

of solving systems of equations and inequalities are introduced at the end of
the semester.

**Objectives:** After finishing the course students should have a good understanding
of the concept of a

function, its domain and range. They should be able to graph basic functions and
be familiar with

their properties. They should be able to perform operations on functions , form
composition and find

the inverse of some one-to-one functions. They should know and be able to apply
properties of

logarithms. They should be able to solve exponential and logarithmic equations
and systems of

equations and inequalities .

**
Organization of the course: **The class meets either twice a week
(Tuesday/Thursday) for 75 minutes

or three times per week (Monday/Wednesday/Friday) for 50 minutes. In a regular semester there are

about 28 75-minute and 42 50-minute lectures. A suggested pace is outlined below. The schedule

allows for in-class exams: three 75-minute exams for 2-day schedule and five 50-minute exams for 3-

day schedule. At least two exams must be given before the drop date. The last exam must cover

exponential and logarithmic functions The 2.5 hour final exam is comprehensive and mandatory for

all students. All sections will have a common departmental final.

**The final exam must count for**

25% of the final grade.

25% of the final grade.

The exams are to test students’ knowledge and ability to perform specific tasks, so open book/notes,

formula sheets/cards are not allowed.

**Graphing calculators are prohibited in this course**and the

use of scientific calculators should be reduced to minimum .

The suggested homework assignment is attached, but some students might need more practice so

assign as many problems as you feel is necessary.

**Suggested pace**

( the number of lectures for a 2-day schedule is given, the corresponding number for a 3-day

schedule is in parenthesis )

**Chapter R - 4.5 (6) lectures**

Sec R.2 (objectives 5 and 6 only)

Sec R.4

Sec R.5

Sec R.7

Sec R.8

**Chapter 2 - 3 (4) lectures**

Sec 2.1

Sec 2.2 (optional : testing an equation for symmetry) together with 1.2

( when finding intercepts use examples that lead to quadratic equations, review methods of solving

such equations (factoring, square root method ), then assign homework from both sections )

Sec 2.3

Sec 2.4 (you can use the general equation of a circle to find intercepts as means of reviewing solving

equations by using quadratic formula; assign problems from sec 1.2 dealing with such equations)

**Chapter 3 – 6 (8) lectures**

Sec 3.1 (make sure to discuss the difference quotient; Ex # 73-80)

Sec 3.2

Sec 3.3 (Optional: local maxima and minima; do not cover objective 5 and the secant line)

Departmental handout : More on Functions (attached) and Sec 5.4 (review sec 5.4 while covering

departmental handout and then assign homework from the handout and sec 5.4; problems on the

handout that lead to quadratic equations can be assigned as supplemental HW)

Sec 3.4 (skip greatest integer function)

Sec 3.5

Sec 3.6

**Chapter 4 – 2 (4) lectures**

Sec 4.3 (emphasize objectives 3 and 4)

Sec 4.4 (objective 1 only)

Sec 4.1 optional (cover objectives 1-3 very briefly)

Sec 4.5 optional (can be combined with 4.4; show 1-2 examples)

**Chapter 5 – 1.5 (3) lectures**

Sec 5.2 (omit oblique asymptotes)

Sec 5.3

**Chapter 6 – 6 (10) lectures**

Sec 6.1 (make sure to cover examples 6,7)

Sec 6.2

Sec 6.3

Sec 6.4 (make sure that students understand what a logarithm to the base a of b is;

discuss the domain of logarithmic functions)

Sec 6.5

Sec 6.6 (objectives 1 and 2 only)

Sec 6.7

Sec 6.8 optional (if you omit this section, make sure to assign some word problems from sec 6.3 and

6.4)

**Chapter 12 – 2 (3) lectures**

Sec 12.1 (objectives 1-4 only; make sure that students understand what the solution of a

dependent system is ; cover some word problems)

Sec 12.6

Sec 12.7

**MORE ON FUNCTIONS
**

For problems 1-19, find the domain of the function

For problems 20-25, find the x-intercepts, if any

26) Find values of x for which the graph of
lies below the x-axis.

27) Find values of x for which the graph of f (x) =| 2x + 3 | lies below the
graph of g(x) = 4.

28) Find values of x for which the graph of f (x) =| 4 − 2x | lies below the
graph of g(x) = 6.

29) Find values of x for which the graph of f (x) =| 7 − x | lies above the
graph of g(x) = 1.

30) Find values of x for which the graph of f (x) =| 5x + 8 | lies above the
graph of g(x) = 2.

**ANSWERS**

**Suggested Homework Assignment**

section | problems |

R.2 | 73-94, 95, 103, 105 |

R.4 | 17, 21, 23, 25,29,35,37,39,43, 45,49,55,57,59,67,71,75,79, 84,87,93,95,99 |

R.5 | 9,11,13,15, 17,21 25,27,33-38,39, 43,45,51, 53,54,57,59,63,86,91,93,95,96,99,105,107, 109,117, 119,121, 123 |

R.7 | 5,8,11,13,15,19,21,23,25,28,31,33,37,41,43,47,49,51,61-71,73,75,76,81,85,87 |

R.8 | 7,12,15,17,18,21,23,25,29,31,33,37,41,43,47,48,49,51,53,55-74, 77,81 |

2.1 | 11,15,19,24,35,45,47 |

2.2 + 1.2 |
11, 21,31,39,40, 41,43, 51-54, 59,61,63,68 find intercepts only unless covering tests for symmetries 13, 15, 21, 29, 31, 21, 42, 47, 55, 79, 85, 89 |

2.3 | 13, 21,23, 25,27,29,
37,39,41,43,47,49,53,55,57,61,63,64, 67,69,70,77,83,85,89, 93, 103,104,105 |

2.4 | 7,9,11,15,21,23,25,27,31 |

3.1 | 15,17,19,21,27,31,32,36,40,43,45,47-60,65,68,70,73,75,79,80,81,87,90 |

3.2 | 9,10,11,12,13,18,20,25 |

3.3 | 11-20, 21,23,25,27,35,36,42,53 29, if covering extrema |

5.4 | 3, 5, 7, 11, 13, 21, 23, 25 |

3.4 | 17-38, 41, 42, 43, 47, 49 |

3.5 | 7,9,11, 13,19-22,24,25, 29, 35,37,39,44,46,47,51,53,55,65a-e, |

3.6 | 1a-c, 7a-b,11a-b, 18 |

4.1(optional) | 17,18, 19, 37, 39 |

4.3 | 17, 27,3235,41,43,45,47,57, 61,65,81,86 |

4.4 | 5,7,9,11,19 |

4.5(optional) | 3,7, 9, 11,13,15, 17, 19 |

5.2 | 13,15,17,20,23-28a-d,35,36,39, 41-52(omit oblique asymptotes) |

5.3 | 7,9, 11, 19,20,23, 33, 35,37 |

6.1 | 11,17,21,27, 35,41,49, 53-58 |

6.2 | 9,11,17,19,23, 33,37,41,42, 57, 61,65 |

6.3 | 11,17,18,37,39,45,49, 50,53, 59,63,67,73,79,97,99 |

6.4 | 9,11,15,16,21,23,24,25-36, 37, 43, 45, 47, 51,55,59,71,77,83,87,91,97,99,103,107,117 |

6.5 | 9,11,13,15,17,25,29,37,41,43,45,47,49,51,55,57,59,61,63,65,69 |

6.6 | 6,9,11,15,16,19,21,23,27,29,31,33,39,41,42,49,53,55,59 |

6.7 | 3,5,7,11,15,19,39,43,45, 49 |

6.8(optional) | 1,3,5,9,21 |

12.1 | 19,25,26,27, 29,30, 57,63,64 |

12.6 | 5,7,9,13,15,27,28,29 |

12.7 | 11-19,23,25,29,33,37,43,45,47 |

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