MA112
Fall 2010
Dr. Byrne
MA112 Midterm Coverage
The midterm will cover:
Module 1 Objectives:
Section R.1 The Real-Numbers
Section 1.1 Introduction to Graphing
Section 1.2 Functions and Graphs
Intervals and interval notation. 
Distance and midpoint between two points. 
Equations of circles.
Identify if a graph is a function.
Finding the domain and range of a function given the graph.
Given a function, find the indicated function values.
Module 2 Objectives:
Section 1.5 Linear Equations,
Functions, Zeros and Applications
Finding the slope and y-intercept of a line.
Applications involving linear functions.
Finding and graphing a line given data about that line. 
Finding the line parallel and perpendicular to another line
through a specific point.
Solving linear equations.
Finding the zeros of linear equations.
Section 1.6 Solving Linear Inequalities
Solving linear inequalities, both simple and compound. 
Section 1.3 Linear Functions, Slope,
and Applications
Section 1.4 Equations of Lines and
Modeling
Module 3 Objectives:
Section 2.1 Increasing, Decreasing
and Piecewise Fns
Section 2.2 The Algebra of
Functions
Graphing a piecewise function.
Find the sum, difference, product or quotient of functions and find
their domain. 
Calculate a difference quotient.
Section 2.3 Composition of
Functions
Finding the composition of two functions. 
Finding the decomposition of a function.
Section 2.4 Symmetry and
Transformations
Graph and/or write the equation for a function that has been
shifted or stretched.
Module 4 Objectives:
Section 3.1 The Complex Numbers
Add, subtract and multiply complex numbers. 
 The starred objectives were covered in class quizzes.
MA112 Midterm Review Questions
Module 1: Intervals and interval notation. 
1. Consider the interval described by the set
x | 4  x  1.
a. Sketch the interval on the real line.
b. Write interval notation for the set.
2. Consider the interval described by the given graph:
a. Write interval notation for the set.
b. Describe the interval using set notation.
Module 1: Distance and midpoint between two points. 
3. Find the midpoint of the line segment connecting the points  5,  8 and 1,  13 and the
distance between them.
Module 1: Equations of circles.
4. Plot the circle given by  x  2    y  1  4 . (Hint: check a point by finding y when x=2.)
2
2
Module 1: Finding the domain and range of a function given the graph.
5. Describe the domain and range of each graph using interval notation.
(a) domain:
(a) domain:
(a) domain:
(a) domain:
(b) range:
(b) range:
(a) range:
(b) range:
Find the domain of f (x) .
6.
f ( x)  x  10
7.
f ( x) 
x  10
8.
Module 1: Given a function, find the indicated function values.
9.
f ( x)  x  7  x  3
(a) Find f (10).
(b) Find f ( x  3).
Module 2: Finding the slope and y-intercept of a line.
10. Find the slope and y-intercept of the line given by 5 x  2 y  9  0 .
f ( x) 
1
2  3x
Module 2: Finding and graphing a line given data about that line. 
11. A line has slope -4 and passes through the point (1,1). Find the equation of this line.
12. A line passes through the point (1,1) and (3,4). Find the equation of this line and graph it.
13. A line passes through the point (1,1) and is parallel to the line given by y 
equation of this line.
14. The graph of a line is given in the plot below. Find the
equation of this line in slope-intercept form ( y  mx  b ).
Module 2: Solving linear equations.
15. Solve 5x  2  3x  2x  6  4x .
Module 2: Finding the zeros of linear equations.
16. Find the zero of the function f ( x)  3x  13 .
1
x  8 . Find the
2
Module 2: Solving linear inequalities.*
17. Solve the compound inequality and describe the solution set using interval notation.
 2  2x  1  5
18. Solve the compound inequality and describe the solution set using interval notation.
2x  8 or x  3  10
Module 3: Graphing a piecewise function.
19. Make a hand-drawn graph of the piecewise defined function
  2 x,
f ( x)  
10  2 x,
for x  2
.
for x  2
Module 3: Find the sum, difference, product or quotient of functions and find their domain. 
20. Find the following arithmetic combinations of f (x) and g (x ) :
(a) f ( x)  g ( x)
f ( x)  3x 2  4 x  10
g ( x)  5  x
(b) f ( x)  g ( x)
(c) f ( x)  g ( x)
(d) f ( x) / g ( x)
Module 3: Calculate a difference quotient.
21. Construct and simplify the difference quotient
f  x  h   f ( x)
1
for f ( x) 
.
h
3x
Module 3: Finding the composition of two functions. 
6
1
22. Find the composition ( f  g )( x) for f ( x)  and g ( x) 
. What is the domain
2x  1
x
of ( f  g )( x) ?
Module 3: Finding the decomposition of a function.
23. Find f (x) and g (x ) such that h(x )  ( f  g )( x) .
h( x )  9 x 2  4
Module 3: Graph and/or write the equation for a function that has been shifted or stretched.
24. Write down a function that shifts f (x) two units to the right and 7 units down.
f ( x) 
x
Module 4: Add, subtract and multiply complex numbers. 
25. Compute and simplify the following. Write answers in the form a  bi .
a.
b.
c.
d.
 1  i    3  i 
 3  4i   8  i 
1  3i   1  4i 
5  3i
4  3i