1
Objective: TSW graph exponential
functions and identify the domain and
range of the function.
๎
A function is called an exponential
A function is called an exponential A function is called an exponential
A function is called an exponential
function if it has a
function if it has a function if it has a
function if it has a
constant
constantconstant
constant
growth/decay factor
growth/decay factorgrowth/decay factor
growth/decay factor
.
. .
.
๎
An exponential functions graph contains
An exponential functions graph contains An exponential functions graph contains
An exponential functions graph contains
an
an an
an asymptote
asymptoteasymptote
asymptote โ
โโ
โ a line the graph
a line the graph a line the graph
a line the graph
approaches BUT never crosses over (a
approaches BUT never crosses over (a approaches BUT never crosses over (a
approaches BUT never crosses over (a
barrier in the graph)
barrier in the graph)barrier in the graph)
barrier in the graph)
๎
Populations tend to growth exponentially
not linearly.
๎
When an object cools (e.g., a pot of soup on
the dinner table), the temperature
decreases exponentially toward the ambient
temperature.
๎
Radioactive substances decay exponentially.
๎
Viruses and even rumors tend to spread
exponentially through a population (at
first).
๎
If the factor
b
is greater than 1, then we call the
relationship exponential growth
exponential growthexponential growth
exponential growth.
. .
.
๎
If the factor
b
is less than 1, we call the
relationship exponential decay
exponential decayexponential decay
exponential decay.
..
.
๎
The equation for an exponential relationship is
given by
๎
y = ab
y = aby = ab
y = ab
x
xx
x-
--
-h
hh
h
+ k
+ k + k
+ k
b = growth/decay factor
b is ALWAYS the number
with the exponent
a = start amount
If there is no โaโ then
a = 1
h = moves
the graph
left or right
k = moves
the graph up
or down
1.
Identify the โkโ value (this is your asymptote) -
put a dotted line where your asymptote occurs.
2.
Identify the โaโ value and put your pencil on the
y-axis (do not draw a point yet)
3.
Use the โhโ and โkโ value to translate the graph
from a.
4.
Sketch the graph as either growth or decay.
Exponential
Growth Exponential
Decay
1. y = 0.25(3)x2. f(x) = 5(0.5)x
y
x
y
x
