W
,September 07 ,
2023 MATH 110
4 1
.
Exponential Functions
restrictions
define functions f(x) =
a* ; at1 at a = 1 constant
as 0 function
Domain (-0 , %)
base = a
exponents : X
*
for examples : f(x) = 2
2
zX
-
y =
(x)(e+ f(x) =
(1)x
(e)
+
in +:
Of
f(x) =
(9
-
1)
f(x) = (9)
+ (x) = ()
f(x) = 33
f(x) = 27
, Rules of exponents
Product/Quotient Rules of same base Zero exponent
at a ax y 90
+
= =
1
x Any o
Negative exponents Product Rule
(9x)"
a"-
*Y
=
a
Quotient Rule
(a) lab) =
axy
, following facts :
1) Exponential function f(x) =
&" is defined by all R
2) Graphs are continuous
3) Rules of exponents hold true for R
restriction
for example : f(x) 3x(a > 1)
=
Step 1 ·
make a table !
SeeI 927
3/1012
-int
1
J
·
(
i
,
1
)
i 11 I
Y = 0
H A
.
,September 07 ,
2023 MATH 110
4 1
.
Exponential Functions
restrictions
define functions f(x) =
a* ; at1 at a = 1 constant
as 0 function
Domain (-0 , %)
base = a
exponents : X
*
for examples : f(x) = 2
2
zX
-
y =
(x)(e+ f(x) =
(1)x
(e)
+
in +:
Of
f(x) =
(9
-
1)
f(x) = (9)
+ (x) = ()
f(x) = 33
f(x) = 27
, Rules of exponents
Product/Quotient Rules of same base Zero exponent
at a ax y 90
+
= =
1
x Any o
Negative exponents Product Rule
(9x)"
a"-
*Y
=
a
Quotient Rule
(a) lab) =
axy
, following facts :
1) Exponential function f(x) =
&" is defined by all R
2) Graphs are continuous
3) Rules of exponents hold true for R
restriction
for example : f(x) 3x(a > 1)
=
Step 1 ·
make a table !
SeeI 927
3/1012
-int
1
J
·
(
i
,
1
)
i 11 I
Y = 0
H A
.
