COLLEGE ALGEBRA
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.
3.2 Inverse Functions
( Be able to find the inverse of a function represented as a set of points, as a table or as a graph.
( Be able to determine whether two functions are inverses using composition of functions.
( Be able to determine whether a function is one-to-one.
( Be able to find the inverse of a function that is one-to-one algebraically. (Note: You may need to restrict the domain.)
3.3 Transformations of Graphs
( Be able to translate, reflect, and compress or stretch a given relation in the form of a graph or equation.
( Be able to test a relation/function for the three types of symmetry.
( Be able to determine whether a function is even or odd.
3.4 Variation
( Be able to find the equation for direct, inverse and joint variation.
( Be able to find the constant of variation for any type of variation.
( Be able to solve problems involving variation.
4.1 The Remainder Theorem and the 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 is a zero of a polynomial.
( Be able to use synthetic division to factor a polynomial given a factor or a zero of the polynomial.
4.2 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.
( Be able to find the real zeros of a polynomial by factoring.
( Be able to determine whether the graph of a function passes through the x-axis or not at a zero.
3. Zeros of Polynomial Functions
( Be able to use the Rational Zero Theorem to find all possible rational zeros of a given polynomial.
( Be able to use the Descartes’ Rule of Signs to find the possible number of positive and the possible number of negative real zeros of a polynomial.
( Be able to use the Rational Zero Theorem, Descartes’ Rule of Signs and the graph of the polynomial to find all of the zeros of the polynomial, including multiplicity, and be able to write the polynomial as a product of linear factors.
4. The Fundamental Theorem of Algebra
( Be able to use known 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.)
5. Graphs of Rational Functions and Their Applications
( Be able to find the horizontal, vertical and inclined (slant) asymptotes (if they exist) of a rational function.
( Be able to graph a rational function using x- intercepts, the y-intercept and asymptotes of the function. (Watch out for holes.)
5.1 Exponential Functions and Their Applications
( Be able to evaluate an exponential function.
( Be able to graph an exponential function.
( Be able to graph translations of an exponential function, including asymptotes.
5.2 Logarithmic Functions and Their Applications
( Be able to switch an equation between logarithmic form and exponential form.
( Be able to evaluate a logarithmic expression with or without a calculator.
( Be able to find the domain of a logarithmic function.
( Be able to graph a logarithmic function, including translations and asymptotes.
( Be able to solve application problems involving logarithmic functions.
Chapter 3 Review (p. 307) 7, 11, 15, 17, 19, 21, 25, 27, 31, 33, 35, 39, 40, 42
Chapter 3 Test (p. 309) 3, 5, 7, 9, 11, 13, 15
Chapter 4 Review (p. 378) 1, 3, 5, 7, 9, 11, 13, 15, 19, 21, 23, 27, 29, 31, 33, 37, 39, 41, 43, 45, 47, 51, 53
Chapter 4 Test (p. 380) 1, 3, 5, 7, 11, 13, 15, 17
Chapter 5 Review (p. 479) 1, 3, 13, 17, 19, 21, 25, 27, 29, 31
Chapter 5 Test (p. 482) 1, 3, 5, 7
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