Math 121
Review for Test 2
1.(Section 3.1) Functions – their domain and range; finding the value of a function; calculating
sums, differences, products, and quotients of two functions; expressing one variable as a function
of another.
Chapter 3 Review exercises: 1-22
2. (Section 3.2) The graphs of functions; reading information about a function from its graph; the
vertical line test; intervals over which a function is positive or negative, increasing or decreasing;
intercepts.
Chapter 3 Review exercises: 25-28. Section 3.2: 24-26, 40
3. (Section 3.3) Properties of functions: even and odd functions; intervals over which a function
is positive or negative, increasing or decreasing; locating local maxima and minima.
Chapter 3 Review exercises: 29-36. Section 3.3: 13, 14, 16, 17, 20, 22, 23, 25, 26
4. (Section 3.4) Identifying and graphing the basic functions. These include:
f ( x)  x
f ( x)  x
f ( x)  x 2
f ( x)  3 x
f ( x)  mx  b
f ( x)  x 3
1
x
f ( x)  int( x)
f ( x) 
Graphing piecewise defined functions, evaluating piecewise defined functions and writing the
equations of a piecewise defined function, given its graph. Writing the equations for and solving
word problems relating to piecewise defined functions.
Chapter 3 Review exercises: 48, 49, 50, 63-66. Section 3.4: 9-16, 47, 53
5. (Section 3.5) Transforming the graphs of the basic functions learned in section 3.4 by shifting,
reflecting, and stretching. Performing these shifts, reflections and stretches on any given graph.
Chapter 3 Review exercises: 51-62. Section 3.5: 66
6. (Section 3.6) Writing equations describing the situation in word problems as a function of a
given variable. Evaluating functions for given values of the domain.
Chapter 3 Review exercises: 71-78 (omit parts which require graphing calculator)
7. (Section 4.1) Properties of linear functions (slopes, intercepts, intersection points).
Chapter 4 Review Exercises: 1-6. Section 4.1: 32, 38, 40, 42
8. (Sections 4.3 and 4.4) Recognizing quadratic functions. Finding the vertex if the function is
in transformation form. Putting a quadratic function into transformation form by completing the
square. Finding the coordinates of the vertex of a parabola both by putting the equation in
b 
b
, f ( )  . Clearly
2a 
 2a
transformation form and by using the fact that the vertex is at 
understanding the difference between the x value of the vertex and the y value of the vertex.
Writing the equation of a parabola given the vertex and one point. Graphing a given parabola by
transforming the graph of f ( x)  x 2 , as well as by plotting the vertex, x and y intercepts and any
other points needed to define the graph. Writing quadratic functions based on word problems.
Finding both the x value of the vertex and the y value of the vertex. Assigning physical meaning
to the x value of the vertex and the y value of the vertex. Understanding that these values occur at
a maximum or minimum of the function. Evaluating your function at given values of either the
domain or range.
Chapter 4 Review Exercises: 1, 2, 7-27, 38, 39, 41 & 42 (a&b)
9. (Section 5.1) Recognizing polynomial functions and identifying their degree. Knowing the
properties of power functions of even degree and of odd degree. Graphing transformations of
power functions. Graphing a polynomial function by identifying its degree, maximum number of
turning points, zeroes and their multiplicities, where the graph is between zeroes, and end
behavior. Given a graph of a polynomial function, identifying possible equations for the graph
based on degree, turning points, zeroes and multiplicities and end behavior.
Chapter 5 Review Exercises: 1-7, 11-16, 89 (a, b & c)
10. (Section 5.2) The definition of a rational function. Finding the domain of a rational function.
Recognizing and graphing the basic functions f ( x ) 
1
1
and f ( x)  2 . Graphing
x
x
transformations of these basic rational functions. Finding the vertical asymptotes of a rational
function. Finding the horizontal or oblique (slant) asymptotes of a rational function.
Chapter 5 Review Exercises: 19-26. Also Section 5.2: 22-36 (evens), 44.
11. (Section 5.3) Sketching the graph of a rational function using the 7 step process given in the
book:
Factor the numerator and denominator of the rational function, then:
1. find the domain
Cancel any common factors, then:
2. find x and y intercepts
3. test for symmetry
4. find the vertical asymptotes
5. find the horizontal or slant asymptote, and find where the graph crosses it (if it does)
6. determine where the graph is above or below the x axis by dividing the domain up
according to the zeroes of both the numerator and denominator.
7. graph (be sure to check domain)
Chapter 5 review problems 27-34
12. Free resources available on campus:
 Algebra Tutoring Table M-F 9 to 2 (check the schedule on line for specific times)
 CAPS on third floor of Zimmerman
 The student solution manual available at Zimmerman Reserve desk
 Math 107 labs – M: 11 (DSH 233), W: 9 (CENT 1026), or F: 11 (DSH 233).
 Your instructor during office hours, or by appointment.