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