MAT-097 Algebra and Introduction to Functions
A transitional course in mathematics designed to provide the student with a solid algebraic background for further studies in mathematics or the sciences. In addition to reviewing algebraic skills for simplifying expressions and solving equations, this course provides an introduction to the concept of a function. The family of linear functions is introduced. The use of realistic applications and modeling with linear functions is an essential component of this course. This course carries imputed (financial aid) credit. It does not fulfill FLCC’s Mathematics or general elective requirements.
Credits
4 imputed credits
Prerequisite
Placement into Math Level 0 or 1
For more detailed course information view the
Course Outline
Course Description
A transitional course in mathematics designed to provide the student with a solid algebraic background for further studies in mathematics or the sciences. In addition to reviewing algebraic skills for simplifying expressions and solving equations, this course provides an introduction to the concept of a function. The family of linear functions is introduced. The use of realistic applications and modeling with linear functions is an essential component of this course. This course carries imputed (financial aid) credit. It does not fulfill FLCC’s Mathematics or general elective requirements.
Credit Hours
4 imputed creditsSemester(s) Course Will Be Offered
Fall, Spring, Summer, Winter
Prerequisites
Placement into Math Level 0 or 1
Course Learning Outcomes
- Use algebraic skills to simplify and factor expressions.
- Use average rate of change to describe functions, and to model realistic scenarios using linear functions.
- Use and interpret function notation.
- Use algebraic skills to solve equations.
Topic Outline
- General philosophy: emphasize realistic applications wherever possible, particularly in motivating new concepts.
- General outline of topics covered:
- 1. General skills
- a. Evaluating expressions containing exponents
- b. Order of operations with real numbers
- i. From basic expressions (two or three operators) to more involved ones (multiple parentheses and operators)
- c. Algebraic substitution (including applied problems)
- d. Solving first-degree equations
- e. Solving for one variable in terms of another
- 2. Exponents
- a. Applying properties of exponents in both directions, for example:
- i. (x²)³ = x⁶ and x⁶ = (x²)³
- b. Negative exponents
- c. Fractional exponents of the form 1/n, where n is an integer and n ≥ 2
- i. Connection to radicals
- d. Addressing common misconceptions about exponents, for example:
- i. (x + y)² ≠ x² + y²
- ii. (−x)² ≠ −x²
- iii. abˣ ≠ (ab)ˣ
- iv. b⁻ˣ ≠ −bˣ
- e. Solving equations with exponents
- 3. Factoring techniques
- a. Common factor
- b. Difference of two squares
- c. Trinomial factoring
- 4. Quadratic equations (real solutions)
- a. Solving by factoring
- i. Zero product principle
- b. Solving by taking square roots
- 5. Functions
- a. Definition of a function
- b. Four forms: verbal, algebraic, tabular (numeric), and graphical
- c. Function notation
- d. Evaluating functions
- e. Average rate of change (calculation and interpretation)
- f. Solving for the input of a function given an output
- g. Interpreting the realistic meaning of the inputs and outputs of a function
- h. Stating the domain and range of realistic functions, and stating just the domain of abstract functions
- 6. Linear functions
- a. Defining property: constant average rate of change (calculation and interpretation)
- b. Forms: point-slope, slope-intercept, and general
- c. Converting between the forms listed in 6b
- d. Finding the slope and the horizontal and vertical intercepts algebraically and graphically
- e. Interpreting the realistic meaning of the slope and the horizontal and vertical intercepts
- f. Modeling with linear functions
- g. Solving linear equations algebraically and graphically
- h. Solving systems of linear equations algebraically and graphically
- i. Algebraically by substitution and elimination
- ii. Dependent and inconsistent systems