MHF 4U1
Chapter 8
EXPONENTIAL FUNCTIONS REFERENCE PAGE
Part 1: Review of Exponential Functions
Allowable values for 𝒃:
𝒚 = 𝒃𝒙
𝑏∈ℝ
𝑏>0
𝑏≠1
➢ When 𝑏 > 0, the graph is _______________________
➢ When 0 < 𝑏 < 1, the graph is ____________________
Properties of Exponential Graphs 𝒚 = 𝒃𝒙
➢ 𝑦 – intercept
➢ Equation of the asymptote:
➢ Domain
➢ Range
➢ For a quick graph use two key points:
Example Graphs
𝒚=𝟐
𝒙
Key points:
𝟏 𝒙
𝒚=( )
𝟑
Key points:
MHF 4U1
Unit 5
Introduction to Logarithmic Functions
Part 2: The Logarithmic Function
a) Find the equation of the inverse of 𝑓(𝑥) = 2𝑥 .
b) Graph both 𝑓(𝑥) and 𝑓 −1 (𝑥).
𝑓(𝑥) = 2𝑥
𝑥
𝑦
MHF 4U1
Unit 5
Introduction to Logarithmic Functions
Part 3: Writing Equivalent Exponential and Logarithmic Expressions
Exponential equations can be written in logarthmic form and vice versa.
𝑦 = 𝑏𝑥 →
𝑦 = log 𝑏 𝑥 →
Ex. Rewrite each equation in logarthmic form.
a) 16 = 24
b) 𝑚 = 𝑛3
c) 3−2 =
Ex. Rewrite each equation in exponential form.
a) log 4 64 = 3
b) 𝑦 = log 𝑥
1
9
MHF 4U1
Unit 5
Introduction to Logarithmic Functions
Part 4: Evaluating Logarithms
Evaluate each logarithm without a calculator.
Rule: If 𝒙𝒂 = 𝒙𝒃 , then 𝒂 = 𝒃.
a) 𝑦 = log 3 81
c) 𝑦 = log (
1
)
100
Rule: 𝐥𝐨𝐠 𝒂 (𝒂𝒃 ) = 𝒃
b) 𝑦 = log 4 256
1
d) 𝑦 = log 2 ( )
32
HW: p.p.451 #1ad, 2, 5 - 11