6th (NEW) EDITION OF THE BOOK

Math 165 - Section 3.1 – Linear Functions and Models

1)  Given a linear function

  1. Graph
  2. Find the slope and y-intercept
  3. Give domain and range
  4. Find x-intercept
  5. Determine whether the line is increasing, decreasing or constant

2)  Recognize tables of linear functions

3)  For linear function given in any form (tables, equations, graphs), solve the common problems:

  1. Given x, find y
  2. Given y, find x
  3. Solve equations
  4. Solve inequalities

4)  Solve word problems involving linearly related data:

  1. Cost function
  2. Revenue, cost and profit functions. Break-even point
  3. Supply and demand
  4. Straight-line depreciation problems - (Vocabulary: useful life, book value)
  5. Scatter diagrams

Section 3.2 – Building Linear Models from Data-

5)  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

6)  Interpret the slope within context

Section 3.3 – Quadratic Functions

7)  Given a quadratic function in Vertex (or Standard Form) , transform the equation to general form

8)  Given a quadratic function in General Form , transform the equation to vertex form

·  By completing the square

·  By finding the coordinates of the vertex with the formula

9)  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

·  Transform the equation to vertex form

·  Solve f(x) = # and identify the point on the graph

·  Find f(#) and identify the point on the graph

·  Write the equation of the axis of symmetry

·  Find the maximum/minimum value of the function analytically

·  Give intervals where the function is increasing/decreasing

·  Check with a graph in the calculator

10) Match quadratic equations and graphs

11) Find the quadratic function when they give you the vertex and another point on the graph

12) Solve word problems involving quadratic functions

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

Section 3.4 – Building Quadratic Models

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

a.  Given the Demand equation, write the Revenue equation and optimize the revenue

b.  Revenue as a function of number of units, x

c.  Revenue as a function of price per unit, p

d.  Enclosing the most area with a fence

e.  Constructing Rain Gutters

f.  Finding the quadratic function that best fits the given data (quadratic regression with the calculator)

14) 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

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

15) Solving quadratic inequalities:

a)  From a graph

b)  With the calculator

c)  Using algebra

16) Word problems involving quadratic inequalities:

17) Find domain of square root functions in which the radicand is a quadratic function

Section 4.1 – Polynomial Functions and Models

1)  Know the properties of Power functions

a)  With even exponent

b)  With odd exponents

2)  Graph transformations of power functions

3)  Identify Polynomial Functions and their degree

4)  Write a polynomial function given its zeros and degree

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

a.  Degree, leading term, leading coefficient

b.  End behavior

c.  Maximum number of turning points

d.  y-intercept

e.  x-intercept(s)/zeros and multiplicity

f.  whether the graph crosses, bounces, or has an inflection point at each of the zeros

g.  sketch the graph

h.  use the calculator to find the maximum, minimum points

i.  give intervals of increase/decrease

j.  find the domain and range

6)  Construct a polynomial function with the given zeros and having a given y-intercept.

7)  Write a polynomial function given its graph

8)  Use the calculator to find the polynomial function that best fits the data

Enter data; Construct the scatter diagram; Observe its shape and decide whether you will fit the data with a Linear, quadratic, cubic or quartic function

Math 180 – Section 4.2, 4.3 (these are 4.5, 4.6 in old edition) - The Real and Complex Zeros of Polynomial Functions We just covered a few topics

9)  Find all the zeros (real and complex) of a polynomial functions (mixing 4.2 and 4.3 here)

10) Solve polynomial equations and inequalities

HERE ARE THE STEPS DONE IN CLASS

a)  List potential rational zeros of f(x)

b)  Enter function in Y=

c)  Graph and identify the rational zeros (x-intercepts that are rational numbers – should be numbers from the ones listed on part (a))

d)  From the rational zero, produce the factor

e)  Do long division to find the missing factor

f)  Use the missing factor to find the remaining zeros which will be

  1. Irrational numbers (they come in pairs of conjugates)
  2. Complex numbers (they come in pairs of conjugates)

Math 180 – Section 4.3 (this is 4.6 in old edition) – Complex Zeros (real numbers are also complex numbers)

11) Given some of the complex zeros of a polynomial function, find the remaining zeros

12) Form a polynomial with real coefficients having the given degree and zeros

13) Use the given zero to find the remaining zeros of the function

14) Find all the zeros of the given polynomial function

Math 180 - Section 4.4, 4.5 (these are 4.2, 4.3 in old edition) –Rational Functions

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

a.  Domain

b.  Vertical asymptote, if any

c.  Horizontal asymptote, if any

d.  X-Intercepts

e.  Y-Intercepts

f.  Coordinates of a hole, if any

g.  Oblique asymptote, if any

h.  Sketch the graph

i.  Range (look at the graph)

j.  Check the graph using the calculator

19) Construct rational functions according to some given characteristics

20) Solve word problems involving rational functions

a)  Minimizing cost

b)  Minimizing surface area

Section 4.6 (it was section 4.4 in the old edition) –Polynomial and Rational Inequalities

21) Solve polynomial inequalities GRAPHICALLY and by finding the boundary numbers and testing signs around them

22) Solve rational inequalities GRAPHICALLY and by finding the boundary numbers and testing signs around them

23) Solve word problems involving polynomial and rational inequalities

1