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Michigan State University | MATH 103
Professors
- James,
- Powers,
- Deyneha,
- Pak,
- Allen,
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- Nancy Nelson,
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- Pearlstein,
- Sue Allen
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50 sample documents related to MATH 103
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Michigan State University MATH 103
4.1 Exponential Functions (Textbook Homework: 1-17(odd), 19-24, 25, 29, 33, 39-57(odd), 65-73(odd), 87-91) Objectives: evaluating exponential function graphing exponential functions evaluating functions with base e using compound interest formulas An -
Michigan State University MATH 103
MTH 103 Exam #3 Review Packet 1. Let f ( x) x2 5 and g ( x) Name_ 3 x . Find each of the following. (a) ( f g )(x) (b) f (x) g (c) dom( f g) (d) dom( g / f ) (e) dom( f g ) (f) dom( g f ) 2. Let f ( x) x 4 and g ( x) 9x 2 . Find each -
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Michigan State University MATH 103
Math 103, College Algebra Syllabus Course Web page: http:/www.math.msu.edu/mth103 Section: Instructor: Office hours: Phone: E-mail: Texts: Spring 2009 College Algebra Essentials by Robert Blitzer, Prentice-Hall, Inc. 2007 Graded Homework Assignment -
Michigan State University MATH 103
Math 103, College Algebra Syllabus Evening Classes Course Web page: http:/www.math.msu.edu/mth103 Section: Instructor: Office hours: Phone: E-mail: Texts: Spring 2009 College Algebra Essentials by Robert Blitzer, Prentice-Hall, Inc. 2007 Graded Ho -
Michigan State University MATH 103
Selected Skill Review Problems for Exam 3 1. Solve the following inequalities algebraically: a) 2(6 2x) 15 b) |3x 7| > 9 c) 2| 4x + 5| 18 d) 3 < x+5 4 2 2. Solve the following inequalities algebraically or graphically: a) x2 5x 6 b) x3 6 < -
Michigan State University MATH 103
Selected Skill Review Problems for Exam 1b 1. Consider the following graph of a function f (x) (each tick mark equals one unit): a) What is the common (base) function? b) What is sequence of transformations needed to obtain f (x) from the common fun -
Michigan State University MATH 103
Math 103 Section 62 Quiz 5 Name: PID: 1. (3 points) Solve the following inequality and sketch the solution on the real number line: -2 2-x <3 5 2. (2 points each) Solve the following inequalities: a) |1 - 2x| < 5 b) x2 - 6x + 9 < 16 1 3. (3 po -
Michigan State University MATH 103
Math 103 Section 62 Quiz 6 (10 points) Name: PID: 1. (3 points) One thousand tickets to the circus were sold. The tickets for adults cost $5 each, and the tickets for children cost $2.50 each. The total receipts for the performance were $3600. How -
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Michigan State University MATH 103
Selected Skill Review Problems for Exam 4 1. Evaluate the following. Give exact (numeric) answers when possible. a) log5 125 b) log2 1 8 c) log16 4 d) log4 7 64 e) log4 32 2. Write the following logarithmic equations in exponential form: a) log2 3 -
Michigan State University MATH 103
Selected Skill Review Problems for Exam 2 1. Solve for x algebraically: - 1 3 3 + = x + 3 5(x - 2) (x + 3)(x - 2) 2. Use a graphing utility to estimate the solutions of: 5 3 =1+ x x+2 3. Solve without a graphing utility: x 2 + =4 x+2 x+2 4. Solve fo -
Michigan State University MATH 103
Section 3.6 Polynomial and Rational Inequalities *Solving Polynomial Inequalities Example 1) Solve and graph the solution set: x 2 - x > 20 . x 0 x 0 Step 1 Express the inequality in the form f( )< or f( )> . x 0 Step 2 Solve the equation f( )= . S -
Michigan State University MATH 103
Review Problems for Exam #3 1. Let ( ) = -2 2 + 12 - 22 . a) Determine whether f (x ) has a maximum or a minimum and find the maximum or minimum value of f (x ) and where it occurs. b) Graph the function f (x) and determine the function\'s domain, r -
Michigan State University MATH 103
Review Problems for Exam #2 1. Determine whether each equation defines y as a function of x. (a) x + y 3 = 0 (b) x + y 2 - 1 = 0 2. Which of the following graphs represent functions? y y y x x x 3. Let f ( x) = x 2 - 4 x + 5 . Find the following -
Michigan State University MATH 103
Chapter 2.8 Distance and Midpoint Formulas; Circles *The Distance Formula The distance, d, between the points ( x1 , y1 ) and ( x 2 , y 2 ) in the rectangular coordinate system is d = ( x 2 - x1 ) 2 + ( y 2 - y1 ) 2 . Example 1) Find the distance be -
Michigan State University MATH 103
Syllabus Instructor Email Website Office hours MTH 103 Section 095 Greg Kehrier kehrierg@msu.edu www.math.msu.edu/~kehrierg A546 Wells Hall, MWF 10:20 11:20 Spring 2008 Teaching Assistant Lauren Herrala Email Required Meetings Normal classes: Tut -
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Michigan State University MATH 103
Review for Exam #3 3.1 Quadratic Functions 2 () a b c x A quadratic functions is any function of the form f x=x+ +, where a, b, c are . real numbers with a 0The graph of a quadratic function is a parabola. >, If a 0 The graph opens upward and has the -
Michigan State University MATH 103
Section 2.3 Linear Functions and Slope *The Slope of a Line The slope of the line through the distinct points ( x1 , y1 ) and ( x 2 , y 2 ) is Change in y Rise y 2 - y1 m= = = Change in x Run x 2 - x1 where x 2 - x1 0 . y x Example 1) Find the sl -
Michigan State University MATH 103
Section 1.3 Models and Application * Problem Solving with Linear Equations Example 1) Basketball, bicycle riding, and football are the three sports and recreational activities in the United States. In 2004, the number of injuries from basketball exce -
Michigan State University MATH 103
Section 3.2 Polynomial Functions and Their Graphs *Definition of a Polynomial Function Let n be a nonnegative integer and let a n , a n -1 , , a 2 , a1 , a 0 be real numbers, with a n 0 . The function defined by f ( x) = a n x n + a n -1 x n -1 + + -
Michigan State University MATH 103
Chapter 2.6 Combinations of Functions; Composite Functions * Finding a Function\'s Domain The domain of a function f is the largest set of real numbers for which the value of f (x) is a real number. Exclude the numbers, which cause Division by Zero an -
Michigan State University MATH 103
Section 3.1 Quadratic Functions A quadratic function is any function of the form f ( x) = ax 2 + bx + c , where a, b and c are real numbers, with a 0 . * Graph of Quadratic Functions The graph of quadratic function is called a parabola. y Axis of s -
Michigan State University MATH 103
Section 2.5 Transformations of Functions * Graphs of Common Functions Table 2.3 (page 242 on the textbook) * Vertical Shifts Let f be a function and c a positive real number. = x+ is = x The graph of y f( ) c the graph of y f( )shifted c units vertic -
Michigan State University MATH 103
Section 3.5 Rational Functions and Their Graphs *Rational Functions Rational functions are quotient of polynomial functions. Rational functions can be expressed as p ( x) , q ( x) where p and q are polynomial functions and q ( x) 0 . The domain of -
Michigan State University MATH 103
Section 2.4 More on Slope *Slope and Parallel Lines 1. If two nonvertical lines are parallel, then they have the same slope. 2. If two distinct nonvertical lines have the same slope, then they are parallel. 3. Two distinct vertical lines, both with u -
Michigan State University MATH 103
Section 4.1 Exponential Functions *Review: Exponential Rules (Section P.2) The Product Rule b m b n = b m +n The Quotient Rule bm = b m- n bn h The Zero-Exponent Rule b0 = 1 The Negative-Exponent Rule h 1 b- n = n b h The Power Rule (b m ) n = b mn P -
Michigan State University MATH 103
Grading and Partial Credit For starters, here is some simple advice. MTH 103-095 You would be amazed at the number of times students seem to make mistakes because they read their own writing incorrectly. You should write all graded items in PENCIL -
Michigan State University MATH 103
Section 4.2 Logarithmic Functions *The Definition of Logarithmic Functions For > 0 and > 0 , o 1 , y = log b x is equivalent to b y = x . The function f ( x) = log b x is the logarithmic function with base b. *Location of Base and Exponent in Expo -
Michigan State University MATH 103
MTH 103 Guided Reading Assignment 1.1 Graphing Sets of Ordered Pairs Name _ I. The Cartesian Coordinate System, Viewing Rectangles We have already discussed how to graph sets whose elements are numbers. Next we will review how to graph sets whose -
Michigan State University MATH 103
Section 3.3 Dividing Polynomials; Remainder and Factor Theorems *The Division Algorithm If f (x) and d (x) are polynomials, with ( ) f 0 , and the degree of d (x) is less than or equal to the degree of f (x) , then there exist unique polynomial q (x -
Michigan State University MATH 103
Math 103 Section 62 Quiz 9 (10 points) Name: PID: 1. Consider the following function: f (x) = log4 (x + 7). a) (1 point) What is the domain of f ? b) (2 points) Find the vertical asymptote and x-intercept of f . 2. (1 point each) Evaluate the fol -
Michigan State University MATH 103
Math 103 Section 62 Quiz 8 (10 points) Name: PID: 1. (2 points) Sketch a graph of the exponential function f (x) = 2x+2 - 4 (you may use a graphing utility if you like). Identify any asymptotes and intercepts of the graph. 2. (1 point each) True o -
Michigan State University MATH 103
Section 3.4 Zeros of Polynomial Functions *Rational Zero Theorem p p (where is reduced q q to lowest terms) is rational zero of f , then p is a factor of the constant term, a 0 , q is a factor of the leading coefficient, a n . Factors of a0 Possible -
Michigan State University MATH 103
Review for Exam #4 0 ( ) 14 0 2x 7 e 1. The equation f x= . 8. 07 describes the average hourly wage for construction workers x years after 2000. Estimate (to the nearest cent) the average hourly wage in 2010. x 3 2. Find the equation represents the
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