Do Now 11/10/09
Copy
HW in your planner.
Text
In
p.266 #4-34 even & #38
your notebook, explain in your own words the
meaning of a function. What do functions consist
of? How are functions different from equations?
Objective

SWBAT use function notation and
graph functions
Section 4.7 “Graph Linear Functions”
Function Notationa linear function written in the form
y = mx + b where y is written as a function f.
x-coordinate
This is read
as ‘f of x’
f(x) = mx + b
slope
y-intercept
f(x) is another name for y.
It means “the value of f at x.”
g(x) or h(x) can also be used to name functions
Linear Functions
What is the value of the function
f(x) = 3x – 15 when x = -3?
A. -24
B. -6
C. -2
f(-3) = 3(-3) – 15
Simplify
f(-3) = -9 – 15
f(-3) = -24
D. 8
Linear Functions
For the function f(x) = 2x – 10, find the
value of x so that f(x) = 6.
f(x) = 2x – 10
Substitute into the function
6 = 2x – 10
Solve for x.
8 = x
When x = 6, f(x) = 8
Domain and Range

Domain = values of ‘x’ for which the function is
defined.

Range = the values of f(x) where ‘x’ is in the
domain of the function f.

The graph of a function f is the set of all points
(x, f(x)).
Graphing a Function

To graph a function:
 (1)
make a table by substituting into the
function.
 (2) plot the points from your table and connect
the points with a line.
 (3) identify the domain and range, (if restricted)
Graph a Function
Graph the Function
SOLUTION
STEP 1
STEP 2
Make a table by
choosing a few values
for x and then finding
values for y.
-2 -1
STEP 3
Plot the points. Notice
the points appear on a
line. Connect the points
drawing a line through
them.
f ( x)  2 x  3
x
f(x) = 2x – 3
0
1
2
f(x) -7 -5 -3
-1
1
f ( x)  2 x  3
The domain and
range are not
restricted
therefore, you do
not have to
identify.
Graph a Function
1
–
Graph the function f(x) = 2 x + 4 with domain x ≥ 0.
Then identify the range of the function.
STEP 1
x
0
2
4
6
8
Make a table.
y
4
3
2
1
0
STEP 2
Plot the points.
Connect the points with a ray
because the domain is restricted.
f ( x)  
1
x4
2
STEP 3
Identify the range. From the graph, you can see that all points have
a y-coordinate of 4 or less, so the range of the function is y ≤ 4.
Family of Functions
is a group of functions with similar
characteristics. For example, functions
that have the form f(x) = mx + b
constitutes the family of linear functions.
Parent Linear Function

The most basic linear function in the family of all
linear functions is called the PARENT LINEAR
FUNCTION which is:
f(x) = x
f(x) = x
x
-5
-2
0
1
3
f(x)
-5
-2
0
1
3
Compare graphs with the graph f(x) = x.
Graph the function g(x) = x + 3, then compare it to
the parent function f(x) = x.
f(x) = x
g(x) = x + 3
g(x) = x + 3
f(x) = x
x f(x)
-5 -5
-2 -2
0 0
1 1
3 3
x f(x)
-5 -2
-2 1
0 3
1 4
3 6
The graphs of g(x) and f(x) have the same slope of 1.
Compare graphs with the graph f(x) = x.
Graph the function h(x) = 2x, then compare it to the
parent function f(x) = x.
f(x) = x
h(x) = 2x
h(x) = 2x
f(x) = x
x f(x)
-5 -5
-2 -2
0 0
1 1
3 3
x f(x)
-3 -6
-2 -4
0 0
2 4
3 6
The graphs of h(x) and f(x) both have a y-int of 0.
The slope of h(x) is 2 and therefore is steeper than f(x) with a slope of 1.
Real-Life Functions
A cable company charges new customers $40 for
installation and $60 per month for its service. The cost to the
customer is given by the function f(x) = 60x +40 where x is the
number of months of service. To attract new customers, the
cable company reduces the installation fee to $5. A function
for the cost with the reduced installation fee is g(x) = 60x + 5.
Graph both functions. How is the graph of g related to the
graph of f ?
The graphs of both functions are
shown. Both functions have a slope of
60, so they are parallel. The y-intercept
of the graph of g is 35 less than the
graph of f. So, the graph of g is a
vertical translation of the graph of f.
Homework

Text p.266 #4-34 even & #38