1825_Sept29_notes_part2

1825_Sept29_notes_pa - MTH
1825
sec.
006
 
 Wednesday,
Sept.
29,
2010
 


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Unformatted text preview: MTH
1825
sec.
006
 
 Wednesday,
Sept.
29,
2010
 
 Example:

Find
the
domain
of
each
of
the
following
functions.

Write
your
final
answer
in
 interval
notation.
 
 f ( x) = x + 5 
 
 g( x ) = 3 x 2 − 10 
 a.
 
 
 
 b.
 
 
 
 € €
 
 x+3 c.
 

 
 
 
 d.
 k( x) = x 
 h( x ) = x −5 
 
 
 € €
 
 
 3x − 1 e.
 

 
 
 
 f.
 m( x ) = 2 x − 5 
 j( x) = 4x + 7 
 
 
 € €
 
 
 
 x−4 g.
 p( x ) = 2 
 
 
 
 
 h.
 r( x ) = 12 − x 
 x +1 
 
 € 
 €
 
 
 
 Section
2.7
–
Graphs
of
Basic
Functions
 
 Linear
and
Constant
Functions
 
 A
linear
function
is
a
function
that
can
be
written
in
the
form
 f ( x ) = mx + b ,
where
 m ≠ 0 .
 A
constant
function
is
a
function
that
can
be
written
in
the
form
 f ( x ) = b .
 
 The
graphs
of
linear
and
constant
functions
are
lines.

(A
constant
function
is
a
horizontal
 € € line.)

Why
isn’t
a
vertical
line
a
linear
function?
 € 
 
 Page
5
of
7
 MTH
1825
sec.
006
 
 Wednesday,
Sept.
29,
2010
 
 Graphs
of
Basic
Functions
 
 
 
 
 
 
 
 
 
 
 
 Identity
function:

 f ( x ) = x 
 
 
 D:
 
 
 R:
 
 
 € 
 
 
 
 
 
 
 
 
 
 
 Cubic
function:

 f ( x ) = x 3 
 
 
 D:
 
 
 R:
 
 
 € 
 
 
 
 
 
 
 
 
 
 
 D:
 
 
 
 
 
 Quadratic
function:

 f ( x ) = x 2 
 D:
 
 € 
 R:
 
 
 
 
 Absolute
Value
Function:

 f ( x ) = x 
 D:
 
 
 € R:
 Square
Root
Function:

 f ( x ) = x 
 
 
 
 € R:
 
 
 
 
 
 Reciprocal
Function:

 f ( x ) = D:
 
 
 R:
 1 
 x € Page
6
of
7
 MTH
1825
sec.
006
 
 Wednesday,
Sept.
29,
2010
 
 A
quadratic
function
is
a
function
that
can
be
written
in
the
form:
 f ( x ) = ax 2 + bx + c 

where
a,
b,
and
c
are
real
numbers
and
 a ≠ 0 .
 
 Example:

Identify
whether
the
function
is
constant,
linear,
quadratic,
or
none
of
these.
 
 € 2 2 1 a.

 f ( x ) = x − 7 
 b.

 f ( x ) = c.

 f ( x ) = π − 2 
 d.

 f ( x ) = x 2 − 5 x + 3 
 − 7
 5 5x 2 
 
 
 € € € 
 
 Finding
the
x­
and
y­
intercepts
of
a
function
defined
by
y
=
f(x)
 
 Given
a
function
defined
by
 y = f ( x ) :
 
 The
y‐intercept
is
 f (0) .
 The
x‐intercept(s)
are
the
real
solutions
to
the
equation
 f ( x ) = 0 .
 € 
 Example:

Find
the
intercepts
of
 f ( x ) = 3 x − 6 .
 € 
 € 
 
 € 
 
 
 
 Example:

For
the
function
 y = f ( x ) 
in
the
graph:
 
 a.
 Find
 f (0) .
 
 y = f ( x) 
 € 
 
 Which
type
of
intercept
did
you
find?
 € 
 € 
 
 
 b.
 Find
the
values
for
which
 f ( x ) = 0 .
 
 
 
 € 
 Which
type
of
intercept
did
you
find?
 
 
 
 
 Page
7
of
7
 € € ...
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This note was uploaded on 11/06/2010 for the course MTH 1835 taught by Professor Cioni during the Fall '10 term at Michigan State University.

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