MATH 159 - College Algebra

4 Credit: (4 lecture, 0 lab, 0 clinical) 4 Contact Hours:

Objectives:

1. recognize when relationships are functions.                           
2. use and interpret function notation.
3. represent and analyze functions.
4. evaluate functions and interpret the results.
5. determine the domain and range of a function and recognize restrictions in applied problems.
6. recognize if a function is increasing or decreasing.
7. calculate and interpret the average rate of change.
8. determine if a function is increasing or decreasing using the average rate of change.
9. determine if a function is linear using the average rate of change.
10. describe the concavity of a function using the average rate of change.

Goal 2:  Apply and analyze piecewise functions, inverse functions, composition of functions and transformations of functions.

Objectives:  

1. evaluate, graph, write the formula for and determine the domain and range of piecewise, inverse, composition of and transformations of functions.
2. model real-world applications with piecewise, inverse, composition of and transformations of functions.
3. decompose functions.
4. use inverse function notation and interpret this notation in the context of a problem.
5. distinguish between invertible and noninvertible functions.
6. verify two functions are inverses algebraically through composition.
7. evaluate combinations of functions (determine the sum, difference, product and quotient of two functions defined by formulas, graphs and tables).
8. describe, graph and write a formula of a function given analytically, graphically, numerically or verbally that has multiple transformations.

Goal 3:  Investigate quadratic, power, polynomial and rational functions.

Objectives:   

1. derive formulas for quadratic functions in standard, factored and vertex form, depending on information given, and convert between these forms.
2. model using direct and inverse variation.
3. write formulas for quadratic, power, polynomial and rational functions and describe their unique graphical characteristics.
4. analyze characteristics of quadratic, power, polynomial and rational functions.
5. model and solve application problems involving quadratic, power, polynomial and rational functions.
6. find the inverses of an invertible polynomial and rational functions and when necessary, restrict the domain to find the inverse.
7. analyze characteristic of radical functions.

Goal 4:  Investigate exponential functions.

Objectives:   

1. write, graph, solve and analyze equations for exponential functions given graphically, numerically, or verbally.
2. model and solve application problems involving exponential functions.
3. model compound interest with exponential functions.
4. identify and analyze the nominal and effective annual rates for compounded interest.
5. write and analyze a formula for continuous exponential growth and decay.

Goal 5:  Investigate logarithmic functions.

Objectives:   

1. define log_bx.
2. convert between logarithmic and exponential equations.
3. apply properties of logarithms.
4. use logarithms to solve exponential equations.
5. solve logarithmic equations.
6. convert between functions of the form Q = ab^t in the form Q = ae^kt and identify what each of the parameters represent.
7. graph logarithmic functions and identify qualities of the functions including domain and range.
8. demonstrate an understanding of logarithmic scales.
9. model data with exponential, logarithmic, and logistic functions using regression.  

Goal 6:  Investigate sequences and series.                    

Objectives:  

1. identify sequences as arithmetic, geometric or neither.
2. describe, analyze and write sequences.
3. find and interpret the partial sum of arithmetic series or geometric series using the appropriate formula.
4. compare and contrast finite and infinite series.
5. write the formula for a series, both finite and infinite, using sigma notation.
6. find the sum of an infinite geometric series using the appropriate formula.
7. use finite and infinite geometric series to model real-world situations and interpret the sums in context.