9/19/11 3.4 Equations of Lines
•  Write equations of lines
•  Use linear models to solve problems.
What information is required to define a
line?
1 9/19/11 Equations of lines
When do I use which form ?!?
•  Slope-Intercept:
•  Point-Slope:
•  Standard (General):
2 9/19/11 Rewrite each equation:
a) In slope-intercept form
b) In general form
Equation?
•  Every year the enrollment at a small college decreases by
25 students. If there are 1650 students this year how can
you describe the enrollment in each subsequent year?
3 9/19/11 Examples
1.  On my second quiz I got 25 points. It is my goal to
improve the quiz grade by 5 points for each quiz.
Express the points you receive on the quiz in terms of
the quiz’s number. Determine dependent and
independent variable. Determine the domain and
range.
Examples
3.  Your phone plan has 300 free texts a month. If
you send 20 messages a day how many days will
it be before you run out of your free tms? Express
the number of remaining texts in terms of the day
of the month. What is dependent and what is the
independent variable? What is the domain and
range?
4 9/19/11 Write the equation of the line…
3.6 Relations and Functions
•  Identify the domains and ranges of relations.
•  Determine if relations are functions by inspection.
•  Use function notation and evaluate functions.
•  Identify the domains and ranges of functions.
5 9/19/11 Different ways to describe a function
•  Verbally – sentence describing how the dependent
and independent variable are related
•  Numerically – using a table or list of ordered pairs
•  Graphically – drawing all the ordered pairs on a
coordinate system
•  Algebraically – writing an expression that describes
how one variable depends on the other
Is this relation a function or not?
6 9/19/11 Function Notation
What can the graph tell us?
•  Can I read the value of a function at a given point?
•  If I know the value of the function, can I find the input?
•  Can I read the domain and range?
7 9/19/11 What can the graph tell us?
f(1) =
f(0)=
f(-1)=
For what x is
f(x)=2
f(x)=-1
f(x)=0
Domain
Range
Which graph best describes the situation?
8 9/19/11 Which graph best describes the situation?
Which graph best describes the situation?
9 9/19/11 Which graph best describes the situation?
Which graph best describes the situation?
10 9/19/11 Review
•  Let the function f be defined by
•  Indicate whether the following statements are true or
false:
1. f(x) is never positive.
2. f(x) is never zero.
3. 0 is in the domain of f
4. All negative real numbers are in the domain of f
5. All positive real numbers are in the domain of f
6. 1 is in the domain of f
7. f is never negative.
Find the domain.
11 9/19/11 3.7 Graphs of Functions
•  Sketch graphs of functions.
•  Identify the graphs of basic functions.
12 9/19/11 Quick draw
y=x2
y=(x-2)2
y=-x2
y=x2-2
y=x2 +2
y=(x+2)2
Sketch each graph.
13