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
x2
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
h4  h 

h
 4h
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
56
1
y  14.61  1.17 x  5
y  14.61  1.17 x  5.85
y  1.17 x  8.76
y  1.177   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
