1. College Algebra
Chapter 2
Functions and Graphs

2. Characteristics of a Linear Equation
College Algebra Chapter 2.1 Rectangular Coordinates and the Graph of a Line
Characteristics of a Linear Equation
Exponent on any variable is 1
No variable is used as a divisor
No two variables are multiplied together

3. Linear Equations Terminology
College Algebra Chapter 2.1 Rectangular Coordinates and the Graph of a Line
Linear Equations Terminology
Solution to a linear equation in 2 variables
Input / Output Table
Rectangular coordinate system
Origin
X axis
Y axis
Coordinate plane
Any pair of substitutions for x and y that result in a true equation
Way to organize solutions of linear equations
Consists of horizontal and vertical number lines
Where the horizontal and vertical number lines intersect
The horizontal number line
The vertical number line
Two dimensional plane where functions are graphed

4. Linear Equations Terminology
College Algebra Chapter 2.1 Rectangular Coordinates and the Graph of a Line
Linear Equations Terminology
Quadrants
Gridlines / tick marks
Coordinate grid
Lattice points
Y-intercept
X-intercept
Begin with I in upper right and move counterclockwise
Placed on each axis to denote the integer values
When tick marks are extend throughout the coordinate plane
When both the x and y have integer values
Where the graph cuts through the x axis
Where the graph cuts through the y axis

5. College Algebra Chapter 2
College Algebra Chapter 2.1 Rectangular Coordinates and the Graph of a Line

6. Graph using the intercept method
College Algebra Chapter 2.1 Rectangular Coordinates and the Graph of a Line
Graph using the intercept method
2x+5y=6
3x-6y=18
-2x+y=-7

7. College Algebra Chapter 2
College Algebra Chapter 2.1 Rectangular Coordinates and the Graph of a Line

8. Graph the lines and tell where they intersect
College Algebra Chapter 2.1 Rectangular Coordinates and the Graph of a Line
Graph the lines and tell where they intersect
x=4 y=-2
(4,-2)

9. Slope Formula and Rates of Change
College Algebra Chapter 2.1 Rectangular Coordinates and the Graph of a Line
Slope Formula and Rates of Change
Steepness of a line is referred to as slope
Measured using the ratio
The slope triangle
Slope expresses a rate of change between 2 quantities

10. Slope Formula and Rates of Change
College Algebra Chapter 2.1 Rectangular Coordinates and the Graph of a Line
Slope Formula and Rates of Change
Result is called the slope formula

11. College Algebra Chapter 2
College Algebra Chapter 2.1 Rectangular Coordinates and the Graph of a Line
Use slope formula to calculate slope of lines that contain the following points

12. Positive and Negative Slope
College Algebra Chapter 2.1 Rectangular Coordinates and the Graph of a Line
Positive and Negative Slope
If m>0, then y values increase from left to right
If m<0, then y values decrease from left to right

13. Slope of horizontal and vertical lines
College Algebra Chapter 2.1 Rectangular Coordinates and the Graph of a Line
Slope of horizontal and vertical lines
Horizontal line m=0
Vertical line m=undefined

14. Slope of parallel and perpendicular lines
College Algebra Chapter 2.1 Rectangular Coordinates and the Graph of a Line
Slope of parallel and perpendicular lines
Slope of parallel lines are equal
Slope of perpendicular lines are negative reciprocals

15. Midpoint formula Distance formula
College Algebra Chapter 2.1 Rectangular Coordinates and the Graph of a Line
Midpoint formula
Distance formula

16. Calculate midpoint and distance for each set of points
College Algebra Chapter 2.1 Rectangular Coordinates and the Graph of a Line
Calculate midpoint and distance for each set of points
(-3,-2) and (5,4)
(7,10) and (-3,-10)

17. College Algebra Chapter 2
College Algebra Chapter 2.1 Rectangular Coordinates and the Graph of a Line
Homework pg

18. Relations and mapping notation
College Algebra Chapter 2.2 Relations, Functions, and Graphs
Relations and mapping notation
A relation is a correspondence between two sets

19. Relations and mapping notation
College Algebra Chapter 2.2 Relations, Functions, and Graphs
Relations and mapping notation
The set of all first coordinates is called the Domain
The set of all second coordinates is called the Range

20. Graph the following relation
College Algebra Chapter 2.2 Relations, Functions, and Graphs
Graph the following relation

21. Graph the following relation
College Algebra Chapter 2.2 Relations, Functions, and Graphs
Graph the following relation

22. Graph the following relation
College Algebra Chapter 2.2 Relations, Functions, and Graphs
Graph the following relation

23. Domain uses vertical boundary lines
College Algebra Chapter 2.2 Relations, Functions, and Graphs
A function is a relation where each element of the domain corresponds to exactly one element of the range
Vertical Line Test
If every vertical line intersects the graph of a relation in at most one point, the relation is a function
Domain uses vertical boundary lines
Range uses horizontal boundary lines

24. Domain of rational and square root functions
College Algebra Chapter 2.2 Relations, Functions, and Graphs
Domain of rational and square root functions

25. Function Notation find
College Algebra Chapter 2.2 Relations, Functions, and Graphs
Function Notation
find

26. College Algebra Chapter 2.2 Relations, Functions, and Graphs
Homework pg

27. College Algebra Chapter 2.3 Linear Functions and Rates of Change
Solving for y in linear equations ax+by=c offers advantages when evaluating
When a function has been solved for y (y has been written in terms of x) it is called function form

28. Solve each equation for y, then state the slope and y-intercept
College Algebra Chapter 2.3 Linear Functions and Rates of Change
A linear function of the form y=mx+b, the slope of the line is m, and the y-intercept is (0,b)
Solve each equation for y, then state the slope and y-intercept
3x-2y=18
4x-y=2

29. Finding equations when given the slope and a point
College Algebra Chapter 2.3 Linear Functions and Rates of Change
Finding equations when given the slope and a point

30. Equations in point-slope form
College Algebra Chapter 2.3 Linear Functions and Rates of Change
Equations in point-slope form
Solve for y

31. Equations in point-slope form
College Algebra Chapter 2.3 Linear Functions and Rates of Change
Equations in point-slope form

32. Equations of lines parallel and perpendicular
College Algebra Chapter 2.3 Linear Functions and Rates of Change
Equations of lines parallel and perpendicular

33. Write the equations of the lines parallel and perpendicular to
College Algebra Chapter 2.3 Linear Functions and Rates of Change
Write the equations of the lines parallel and perpendicular to

34. College Algebra Chapter 2.3 Linear Functions and Rates of Change
Homework pg

35. Characteristics of Quadratics
College Algebra Chapter 2.4 Quadratic and other Toolbox Functions
Characteristics of Quadratics
Concavity
Axis of Symmetry
Vertex
Direction branches point, this is the end behavior (concave up or down)
Imaginary line that cuts the graph in half
Highest or lowest point

36. Graphing factorable quadratic functions
College Algebra Chapter 2.4 Quadratic and other Toolbox Functions
Graphing factorable quadratic functions
Determine end behavior: concave up if a > 0, concave down if a < 0
Find the y-intercept by substituting 0 for x:
Find the x-intercept(s) by substituting 0 for f(x) and solving for x
Find the axis of symmetry
Find the vertex
Use these features to help sketch a parabolic graph

37. Graphing factorable quadratic functions
College Algebra Chapter 2.4 Quadratic and other Toolbox Functions
Graphing factorable quadratic functions
Determine end behavior: concave up if a > 0, concave down if a < 0
Find the y-intercept by substituting 0 for x:
Find the x-intercept(s) by substituting 0 for f(x) and solving for x
Find the axis of symmetry
Find the vertex
Use these features to help sketch a parabolic graph

38. Graphing factorable quadratic functions
College Algebra Chapter 2.4 Quadratic and other Toolbox Functions
Graphing factorable quadratic functions
Determine end behavior: concave up if a > 0, concave down if a < 0
Find the y-intercept by substituting 0 for x:
Find the x-intercept(s) by substituting 0 for f(x) and solving for x
Find the axis of symmetry
Find the vertex
Use these features to help sketch a parabolic graph

39. Square root functions Always begin at a node
College Algebra Chapter 2.4 Quadratic and other Toolbox Functions
Square root functions
Always begin at a node
Also called a one wing graph
To graph
Find the node, x-intercept, y-intercept, and an additional point

40. College Algebra Chapter 2.4 Quadratic and other Toolbox Functions
Square root functions
To graph
Find the node, x-intercept, y-intercept, and an additional point

41. College Algebra Chapter 2.4 Quadratic and other Toolbox Functions
Square root functions
To graph
Find the node, x-intercept, y-intercept, and an additional point

42. Cubing Function Have points of inflection / pivot points To graph find
College Algebra Chapter 2.4 Quadratic and other Toolbox Functions
Cubing Function
Have points of inflection / pivot points
To graph find
End behavior
Y-intercept
x-intercepts
Point of inflection
Additional points

43. College Algebra Chapter 2.4 Quadratic and other Toolbox Functions
To graph find
End behavior
Y-intercept
x-intercepts
Point of inflection
Additional points
Cubing Function

44. College Algebra Chapter 2.4 Quadratic and other Toolbox Functions
To graph find
End behavior
Y-intercept
x-intercepts
Point of inflection
Additional points
Cubing Function

45. College Algebra Chapter 2.4 Quadratic and other Toolbox Functions
Cube root function
Graph by selecting inputs that yield integer value outputs

46. College Algebra Chapter 2.4 Quadratic and other Toolbox Functions
Cube root function

47. The average rate of change for a function
College Algebra Chapter 2.4 Quadratic and other Toolbox Functions
The average rate of change for a function
Given that f is continuous on the interval containing x1 and x2, the average rate of change of f between x1 and x2 is given by

48. The average rate of change for a function
College Algebra Chapter 2.4 Quadratic and other Toolbox Functions
The average rate of change for a function
Find the average rate of change for the interval

49. College Algebra Chapter 2.4 Quadratic and other Toolbox Functions
Homework pg

50. College Algebra Chapter 2.5 Functions and Inequalities
Since an x-intercept is the input value that gives an output of zero, it is also referred to as a zero of a function

51. Meaning for what inputs is the graph above or equal to the x axis?
College Algebra Chapter 2.5 Functions and Inequalities
Meaning for what inputs is the graph above or equal to the x axis?
What is the x-intercept?

52. Solving quadratic inequalities
College Algebra Chapter 2.5 Functions and Inequalities
Solving quadratic inequalities
Find zeros of function
Check concavity
Sketch the parabola
State solution

53. College Algebra Chapter 2.5 Functions and Inequalities
Homework pg

54. College Algebra Chapter 2.6 Regression Technology and Data Analysis
Regression is an attempt to find an equation that will act as a model for raw data

55. Scatter Plots & positive / negative Association
College Algebra Chapter 2.6 Regression Technology and Data Anaylsis
Scatter Plots & positive / negative Association
Scatter Plots & linear / nonlinear associations
Strong & Weak Associations
Calculating linear equation model for a set of data
Linear regression and the line of best fit TI-83

56. College Algebra Chapter 2.6 Regression Technology and Data Anaylsis
Homework pg

57. Slope lines Ordered pair scatter-plot Intercept axis of symmetry Range
College Algebra Chapter 2 Review
lines
scatter-plot
axis of symmetry
Origin
y-axis
Input
Vertex
lattice point
Node
Relation
zeros of a function
Slope
Ordered pair
Intercept
Range
x-axis
Output
Function
Domain
parallel lines
Regression
perpendicular

58. College Algebra Chapter 2 Review

59. College Algebra Chapter 2 Review

60. College Algebra Chapter 2 Review

61. College Algebra Chapter 2 Review