A function is called an exponential
function if it has a constant
growth/decay factor.
An exponential functions graph contains
an asymptote – a line the graph
approaches BUT never crosses over (a
barrier in the graph)
Objective: TSW graph exponential
functions and identify the domain and
range of the function.
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.
growth.
If the factor b is less than 1, we call the
relationship exponential decay.
decay.
The equation for an exponential relationship ish = moves
the graph
given by
left or right
y = abx-h + k
k = moves
the graph up
or down
a = start amount
If there is no “a” then b = growth/decay factor
b is ALWAYS the number
a=1
with the exponent
1.
2.
3.
4.
Identify the “k” value (this is your asymptote) put a dotted line where your asymptote occurs.
Identify the “a” value and put your pencil on the
y-axis (do not draw a point yet)
Use the “h” and “k” value to translate the graph
from a.
Sketch the graph as either growth or decay.
Exponential
Growth
Exponential
Decay
1. y = 0.25(3)x
2. f(x) = 5(0.5)x
y
y
x
x
1
3. y = 0.75x
4. f(x) = 4x
5. y = 2x+2 - 3
y
y
7. y = 0.75x+1
y
y
x
x
6. y = 2(0.25)x-1 + 2
x
x
8. f(x) = 2(4)x + 3
y
y
x
x
2