Transcript 1.2 Notes
Students, Take out your calendar and your homework. Take out
your spiral notebook and Complete the DNA. Use your
notes if necessary.
5x 6 y 7 0
1) A line parallel to the
graph of the equation
above has a slope of
___.
2) A line perpendicular
to the graph of the
equation above has a
slope of ___.
Evaluate.
f x x 2 5
3) f 2
4) f 3
5) f 2 a
The domain of a function is the “inputs.”
The range of a function is the “outputs.”
f x x
x
0 1 4 9 7 4 9
f x 0 1 2 3
domain : x 0
7
2i
3i
range : y 0
from the graph
Finding the domain of a function
ex 1) g ( x) x 16
x2
ex 2) h( x) 2
x 9 x 14
Find the domain of the functions.
1) f ( x) 4 x
3) k ( x) 9 x
3
2) g ( x)
x 5
3
4) f ( x) 2
x 4
2
Difference Quotient
For g x x 3,
2
g 2 h 2 h 3
2
4 4h h 3
2
g 2 h g 2
find
.
h
1 4h h 1
4h h
h
h
2
1 4h h 2
2
h4 h
h
4h
5) For f x x 2 x 9, find
2
f (4 h) f (4)
, h 0.
h
6)
a.
b.
c.
f x 2 3x x
f (3)
f ( x 1)
f ( x h) f ( x )
2
for
7) Determine if y is a function of x;
3
2 2
2 x 3x y 1 0
8) Find the domain :
3
f ( x)
x 1
ex) Evaluate the function
3x 5, x 2
f ( x) 2
x 1, x 1
when x 4, 1, and 2.
f (4) 3(4) 5 17
f (1) undefined
f (2) 2 2 1 5
1) Find f (5), f (7 / 2), and f (1)
1 3x 2 , x 2
where f ( x)
5 x 2, x 4
2) Find f (0), f (2), f ( y 3), and f (3x)
3
where f ( x) 2
.
x 4
Ex 4)
The net sales for a car manufacturer were $14.61 billion in 2005
and $15.78 billion in 2006. Write a linear equation giving the net
sales y in terms of x, where x is the number of years since 2000.
Then use the equation to predict the net sales for 2007.
x 0 represents 2000
So, 5, 14.61 and 6, 15.78 are
2 pts on the line
14.61 15.78 1.17
m
1.17
56
1
y 14.61 1.17 x 5
y 14.61 1.17 x 5.85
y 1.17 x 8.76
y 1.177 8.76
y 8.19 8.76
y 16.95
$16.95 billion dollars
for 2007
Graph the following linear functions. Graph #1 – 3 on
the same coordinate plane.
1) 5 x y 4
2) 2 x 10 y 20
3) 10 x 2 y 6
4) y 1
5) x 3
3) Find the slope-intercept
form of the line
2
perpendicular to y x 11
5
(a)passing through (-5, 2)
(b) passing through (1, 3)
Find the domain of the following functions.
1) f ( x) x 3
2) h x x 5
3) g x 4 x
Graph the following functions.
2 x 3, x 3
1) f x
3x 1, x 3
5 x 2, x 2
2) f x 2
x , x 2
2 x, x 1
3) f x 4, 1 x 3
3x, x 3