For the final, you will be allowed two sides of a 3 by 5
note card for notes.
One of the best ways to study for the final is to go over
your old exams and graded work.
This will give you an idea of how problems may be worded and how you will be
graded
on them. Below, I have narrowed down the topics, provided formulas, and listed
practice
problems. Don’t feel like you have to do all of the problems to prepare, but it
is a good
idea to work through ones that you are not yet comfortable with. Most of the
practice
problems listed are from chapter reviews in the book, for which there are
answers (for
both evens and odds) in the back of the book.
Topics that may be covered on the final:
Chapter 1:
1.3
• Solve an absolute value problem. Remember |E| = k if and
only if E = k or
E = −k .
• p. 154 Chapter 1 Review #23-26
• Solve a rational equation . (Multiply all terms by a
common denominator .)
• p. 154 Chapter 1 Review #5-8
• Solve a radical equation and check for extraneous
solutions.
• p. 123 Section 1.3 #43-46
1.4
• Solve an absolute value inequality.
|E| ≤ k if and only if − k
≤ E ≤ k .
|E| ≥ k if and only if E
≤ −k or E ≥ k
• p. 154 Chapter 1 Review #55-58
1.5
• Solve a quadratic or rational inequality.
Get 0 on one side. Solve for zeros of the numerator and denominator separately .
Set up a number line and test points.
• p. 154 Chapter 1 Review #45, 46, 49, 54
Chapter 2:
2.1
• Find the distance between two points.
• p. 246 Chapter 2 Review #15-18
• Find the equation of a circle with center (h, k) and radius r.
• p. 246 Chapter 2 Review #19
2.2
• Identify a function using the vertical line test.
• Identify a one-to-one function using the horizontal line test.
• Like problem 2 on the second exam
2.3
• Given two equations of lines, be able to tell if they are parallel,
perpendicular or neither.
• Are the following lines parallel,
perpendicular, or neither? Explain
2.4
• Given two points, find the equation of the line passing through them.
Slope =
Line in point-slope form:
Then solve for y.
• p. 218 Section 2.4 #17-32
2.5
• Be able to solve a max. or min. application problem, using the vertex
formula .
Given a quadratic
the vertex is at
• p. 248 Ch. 2 Review #76, p. 250 Ch. 2 Test
#13
Chapter 3:
3.1
• Add, subtract , multiply and divide functions.
• p. 307 Chapter 3 Review #1, 2
• Compose two functions. f o g(x) = f (g(x)) .
• p. 307 Chapter 3 Review #3, 4
• Find the difference quotient of a function. The difference quotient of f (x)
is
• p. 307 Chapter 3 Review # 5, 6
3.2
• A function must be one-to-one to have an inverse.
• Domain of a function equals range of its inverse.
Range of a function equals domain of its inverse.
• Use composition to prove that two functions are inverses:
Two functions f and g are inverses if and only if f (g(x)) = x and g( f (x)) = x
.
• p. 307 Chapter 3 Review #25-30
• Find the inverse of a function (p.267).
• p. 307 Chapter 3 Review #31-34
3.3
•Show that a function is even or odd.
A function is even if f (−x) = f (x) . This means f is symmetric about the
y-axis.
A function is odd if f (−x) = − f (x) . This means f is symmetric about the
origin.
• p. 307 Chapter 3 Review #21-24
• Transformations of graphs. Be able to shift, flip and stretch a given
graph.
• p. 307 Chapter 3 Review #7-12, 14
3.4
• Solve an application problem using direct or inverse variation.
Solve for the constant of variation, k, then use k to find the answer to the
question.
• p. 307 Chapter 3 Review #39, 40
Chapter 4:
4.1
• Use synthetic division to divide polynomials.
• p. 378 Chapter 4 Review #1-6
4.3
• Use the Rational Zero Theorem to find all possible rational zeros of a
polynomial.
• p. 378 Chapter 4 Review #21-26
4.4
• A polynomial of degree n has exactly n roots.
• Find all zeros of a polynomial.
• p. 378 Chapter 4 Review #34, 36 (set up like
the problem on test 3)
• Given one complex root of a polynomial, use the Conjugate Pair Theorem to find
the other roots.
• p. 378 Chapter 4 Review #37, 38
4.5
• Find the vertical asymptotes and domain of a rational function. (Find the
zeros of the denominator.)
• Find the horizontal asymptotes of a rational function.
• Find the slant asymptotes of a rational function.
• p. 378 Chapter 4 Review #43-46
Chapter 5:
5.2
• Graph a logarithmic function or its translation. If
remember that
• p. 479 Chapter 5 Review #19-21
• Find the domain of a logarithmic function .
•
Find the domain of
• Write a logarithm in exponential form or an exponential in log form.
•
p. 479 Chapter 5 Review #25-32
• Remember that f (x) = bx and g(x) = logbx are inverses, thus their
composition
results in x (the input).
5.3
• Use the properties of logarithms (stated on p. 414) to:
a. Rewrite a single logarithm as several logarithms.
• p. 479 Chapter 5 Review #33-36
b. Combine several logarithms into one.
• p. 479 Chapter 5 Review #37-40
5.4
• Solve exponential and logarithmic equations. Give exact
answers.
• p. 479 Chapter 5 Review #45-60
Chapter 6:
6.1
• Solve a system of two equations
• Recognize a system with no solutions.
• Recognize a system with infinitely many solutions and write the answer in
terms of one of the variables.
• p. 572 Chapter 6 Review #1-8
6.2
• Solve a system of three equations.
• Recognize a system with no solutions.
• Recognize a system with infinitely many solutions and write the answer in
terms of one of the variables.
• p. 572 Chapter 6 Review #9-18
6.3
• Give the order of a matrix.
• Put a system of equations into an augmented matrix.
• Write the coefficient matrix and the constant matrix for a system of
equations.
• Write a system of equations from a matrix.
• Perform elementary row operations .
• Solve a system of equations using a matrix.
• Recognize a matrix that tells that a system of equations has no or infinitely
many solutions.
• See chapter 6 test review (handout) for examples
6.4
• Add, subtract, and multiply matrices.
• p. 572 Chapter 6 Review #39-46
