Graphing Exponential Functions
Guided Notes
Math I
Name: _________________________________
Date: _________________________________
Learning Targets




I can graph exponential functions using a table.
I can describe the transformation of an exponential function from its parent function.
I can state the domain and range of an exponential function.
I can determine whether a function is linear or exponential.
Exponential Functions

An exponential function is a function of the form 𝑦 = 𝑎 ⋅ 𝑏 𝑥 – that is, a function in which the variable is
an exponent.
Exponential functions either increase at an increasing rate (increase faster and faster) or decrease at a
decreasing rate (decrease slower and slower).
In this class, we will graph exponential functions using a table.


Example:
Graph 𝑦 = 2𝑥
x
-2
-1
0
1
2
3
y
0.25
0.5
1
2
4
8
𝑦 = 2−2 = 0.25
𝑦 = 2−1 = 0.5
𝑦 = 20 = 1
𝑦 = 21 = 2
𝑦 = 22 = 4
𝑦 = 23 = 8
Examples (graphing exponential equations):
a)
𝑦 = 3𝑥
𝒙
-2
-1
0
1
2
𝒚
y-intercept: ___________________
Domain: ___________________
Range: ___________________
1 𝑥
𝑦 = (3)
b)
𝒙
-2
-1
0
1
2
𝒚
𝒙
-2
-1
0
1
2
Domain: ___________________
Range: ___________________
𝑦 = 3(2)𝑥
c)
y-intercept: ___________________
𝒚
y-intercept: ___________________
Domain: ___________________
Range: ___________________
Application
a)
A dangerous type of moss is spreading over a lake. The area of the lake is 250,000 𝑓𝑡 2 . Currently, the moss has
an area of 4 𝑓𝑡 2 . The moss will triple its area every day until a team of scientists fixes the problem.
i)
How large will the area of moss be after 5 days?
ii)
How long will it take for the moss to completely cover the lake?
b)
Daniel invested $500 into a savings account. The equation 𝐴 = 500(1.005)12𝑡 models the value of his
investment 𝐴 after 𝑡 years. How much with Daniel’s investment be worth in 8 years?
c)
The table below gives the population of the world at certain years throughout history. Plot this data on the
scatterplot and answer each of the following questions.
x (year)
y
(population
in millions)
1800
1825
1850
1875
1900
1925
1950
1975
2000
900
1050
1171
1300
1608
1900
2406
4071
6100
i)
What was the world’s population in 1935?
ii)
According to the graph, what will the world’s
population be in 100 years?