Class notes Math110

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
.