Exam 1 Study and Scoring Guidelines
(Math 107 Sections 1-5)


Exam 1 will contain problems that address the following topics.  For each of the seven topics listed below, part b will be weighted as much as parts a and c combined.  For example, of the number of points fixed to a given problem, 50% of the points can be earned by performing well in the conceptual understanding category, 30% may be earned in the basic skills category, and 20% may be earned in the communication category.  

1.    Composition of functions  (3,7,8)

a.)  Basic skills
        Correct use of substitution
        Correctly reading a graph
b.)  Conceptual understanding
        Demonstrated knowledge of evaluating a function
        Demonstrated knowledge of composition of functions
        Correctly identifies and uses combinations of functions
        Recognizes when functions are defined
c.)  Communication skills
        Using correct notation
        Clear graphical representations

2.    Domain and Range  (1,6,9)

a.)  Basic skills        
        Solving inequalities and equations
        Arithmetic skills
b.)  Conceptual understanding
        Know definitions of domain and range
            What's included
            What's not included
        Recognizes undefined functions
c.)  Communication skills
        Using correct notation
        Understand different representations (Numerical, verbal, symbolical, and graphical)

3.    Linear functions  (2,4)

a.)  Basic skills
        Correctly read graphs
        Correctly use substitution
        Correctly use distribution property
        Correctly use property of equality
b.)  Conceptual understanding
        Demonstrate understanding of slope
        Demonstrate understanding of relationship of slope of a line with respect to parallel and/or perpendicular lines
        Using the data (i.e. points) of functions to find constants of functions
        Recognize and use key characteristics of standard forms of functions
c.)  Communication skills
        Explanations are given in clear sentences
        Work shown is orderly and clearly legible

4.    Transformations of graphs  (5)

a.)  Basic skills
        Correctly uses basic math facts
        Correctly uses arithmetic
        Correctly uses graphing techniques    
b.)  Conceptual understanding
        Distinguishes an argument from function value
        Demonstrates knowledge and understanding of all types of graphical transformations
        Vertical and horizontal shifts, reflections in the x and in the y axes, vertical and horizontal stretches and shrinks.
c.)  Communication skills
        Demonstrates understanding and correct usage of notation

5.    Graphing Functions  (6)

a.)  Basic skills
        Correctly plots points on graphs
        Correctly uses arithmetic
b.)  Conceptual understanding
        Understanding of domain and range
        Understanding of how to evaluate a function
c.)  Communication skills
        Uses correct notation
        Correctly labels graphs
        Work shown is orderly and clearly legible

6.    Inverse functions  (9)

a.)  Basic skills
        Reading data on a graph
        Plotting data on a graph
b.)  Conceptual understanding
        Reflection (on the line y=x)
        Exchange of domain and range
c.)  Communication skills
        Correct notation
        Clarity of Representations
        Work shown is orderly and clearly legible

7.    Modeling with functions  (10)

a.)  Basic skills
        Correct use of substitution
        Correct use of property of equality
        Correct use of distribution property
b.)  Conceptual understanding
        Demonstrates knowledge of developing models from data
        Demonstrates understanding of using models
        Demonstrates understanding of maximum and minimum values of quadratic equations
c.)  Communication skills
        Uses correct notation

        Clarity of Representations
        Work shown is orderly and clearly legible