COLLEGE ALGEBRA
EXAM II REVIEW
Read the directions carefully. I want you to SHOW YOUR WORK for each problem. A solution,
even a correct solution, will not receive full credit if there is no support work or explanation.
Partial credit is always considered, so showing your work is to your advantage.
2.5
Properties of Graphs
 Be able to translate (left, right, up, down), reflect (across the x or y axis), and compress or
stretch vertically a given relation in the form of a graph or equation.
 Be able to test a relation or function for the three types of symmetry (x-axis, y-axis, origin).
 Be able to determine whether a function is even or odd or neither.
2.6
Algebra of Functions
 Be able to add, subtract, multiply or divide two given functions, find their domains, and
evaluated them for value(s) of x.
 Be able to find the difference quotient for a given function.
 Be able to compose two given functions, find their domains, and evaluated them for value(s)
of x.
3.1
Remainder Theorem and Factor Theorem
 Be able to use long division to divide a polynomial function by a polynomial divisor.
 Be able to use synthetic division to divide a polynomial function by a linear divisor.
 Be able to use the Remainder Theorem and synthetic division to evaluate a function at a
particular value(s) of x.
 Be able to use synthetic division to show that a particular value of x is a zero of a
polynomial.
 Be able to use synthetic division to determine if a given binomial is a factor of a
polynomial.
 Be able to use synthetic division to factor a polynomial given one of the factors of the
polynomial.
3.2
Polynomial Functions of Higher Degree
 Be able to determine the far-left and far-right behavior of a polynomial function.
 Be able to find the relative maximum(s) and relative minimum(s) of a polynomial function
using your calculator.
 Be able to find the real zeros of a polynomial by factoring.
 Be able to use the Intermediate Value Theorem to show that a polynomial has a zero between two
given values of x.

Be able to determine whether the graph of a function passes through the x-axis or not at an
x-intercept.
 Be able to sketch the graph of a polynomial that is given in factored form.
3.3
Zeros of Polynomial Functions
 Be able to state the multiplicity of a zero of a polynomial that is given in factored form.
 Be able to use the Rational Zero Theorem to list all the possible rational zeros of a given
polynomial.
 Be able to use the Rational Zero Theorem, and the graph of the polynomial to find all of the
zeros of the polynomial, including multiplicity.
3.4
Fundamental Theorem of Algebra
 Be able to find all of the zeros of a polynomial, (first find any rational zeros by graphing the
polynomial on your calculator and using the Rational Zero Theorem and synthetic division),
and write the polynomial as a product of linear factors.
 Be able to use known zeros (including complex zeros) and synthetic division to factor a
polynomial function and find its zeros.
 Be able to find the complex zeros of a polynomial.
 Be able to use information about the degree of a polynomial and its zeros, including
multiplicity, to find the general equation of the polynomial. (Note: If additional information
is given, a particular equation can be found.)
3.5
Graphs of Rational Functions and Their Applications
 Be able to find the domain of a rational function.
 Be able to find the horizontal, vertical and slant asymptotes (if they exist) of a rational
function.
 Be able to graph a rational function using x- intercept(s), the y-intercept and any asymptotes
of the function. (Watch out for holes.)
Chapter 2 Review (p. 253) 71, 73, 75, 77, 79, 81, 83, 87, 89, 91, 96, 97, 100, 101
Chapter 2 Test (p. 257) 12, 13, 19
Chapter 3 Review (p. 328) 1 – 21 odd, 25 – 61 odd (not 33 and 35), 65
Chapter 3 Test (p. 331) 1 – 7 odd, 11, 13, 15, 16