MATH 165 – Chapter 3 Study Guide – 6TH Edition

Section 3.1 – Linear Functions and Models

1)Solve linear equations and inequalities graphically (#29 – 36, pg. 137)

Section 3.2 – Building Linear Models from Data-

1)Draw scatter diagrams with the calculator, distinguish between linear and nonlinear relations, find the line of best fit using the calculator, use the line of best fit to make predictions

2)Interpret the slope within context

Section 3.3 – Quadratic Functions

3)Given a quadratic function in any format

  • Find the coordinates of the vertex analytically
  • Decide whether it opens up or down
  • Graph by hand
  • Find domain and range
  • Find x- and y-intercepts
  • Solve f(x) = # and identify the point on the graph
  • Find f(#) and identify the point on the graph
  • Find the maximum/minimum value of the function analytically
  • Give intervals where the function is increasing/decreasing
  • Check with a graph in the calculator

4)Solve word problems involving quadratic functions

Given a quadratic function, find the “optimal” value of the function

Section 3.4 – Building Quadratic Models

5)Construct the quadratic model for the following types of stories:

  1. Given the Demand equation, write the Revenue equation and optimize the revenue
  2. Revenue as a function of number of units, x
  3. Revenue as a function of price per unit, p
  4. Enclosing the most area with a fence
  5. Constructing Rain Gutters
  6. Finding the quadratic function that best fits the given data (quadratic regression with the calculator)

6)Be able to answer the following types of questions when they give you a word problems

a)For a given x, find y

b)For a given y, find x. Analytically or graphically

c)Questions asking about x-intercepts

d)Answer optimization problems by finding the coordinates of the vertex algebraically.

e)Questions asking about the maximum/minimum point , maximum/minimum value of the function; optimal x, to produce the max/min value of the function

3.5 – Inequalities involving Quadratic Functions

7)Solving quadratic inequalities:

a)From a graph

b)With the calculator

8)Word problems involving quadratic inequalities:

MATH 165 – Chapter 4 Study Guide – 6TH Edition

Section 4.1 – Polynomial Functions and Models

1)Know the properties of Power functions

  1. With even exponent
  2. With odd exponent

2)Identify Polynomial Functions and their degree

3)Write a polynomial function given its zeros and degree

4)For a given polynomial function, determine each of the following:

  1. Degree
  2. End behavior
  3. Maximum number of turning points
  4. y-intercept
  5. x-intercept(s)/zeros and multiplicity
  6. whether the graph crosses, bounces, or has an inflection point at each of the zeros
  7. sketch the graph
  8. use the calculator to find the maximum, minimum points
  9. give intervals of increase/decrease
  10. find the domain and range

5)Construct a polynomial function with the given zeros and going through a certain point.

6)Write a polynomial function

  1. Given its graph
  2. According to some given characteristics

Section 4.2 and 4.3 - The Real and Complex Zeros of Polynomial Functions

7)To find the zeros, do the following:

  1. Think how many complex zeros you are expecting
  2. Graph with the calculator and find all the REAL zeros with the calculator.
  3. If there are irrational (real) zeros or imaginary zeros, I will give you the quadratic factor for you to find them
  4. Write the function as a product of linear factors based on the zeros

Section 4.4, 4.5 –Rational Functions

8)Given a Rational function, find each of the following:

  1. Domain
  2. Vertical asymptote, if any
  3. Horizontal asymptote, if any
  4. X-Intercepts
  5. Y-Intercepts
  6. Coordinates of a hole, if any
  7. Sketch the graph
  8. Describe with symbols:
  9. Local behavior
  10. End behavior

9)Construct rational functions according to some given characteristics

10)Solve word problems involving rational functions (in 4.4: 56, pg. 226, in 4.5: 49. 53’ pg. 235)

Section 4.6 –Polynomial and Rational Inequalities

11)Solve polynomial inequalities graphically and using the “signs” method

12)Solve rational inequalities graphically and using the “signs” method

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