I identify transformations of exponential
and logarithmic functions
Warm Up
1. Solve for x. Use properties when needed
a) 𝑙𝑜𝑔8 𝑥 + 1 = 3
5𝑥−6
b) −4 ∙ 2
= −64
c) 𝑙𝑜𝑔2 3𝑥 + 1 − 𝑙𝑜𝑔2 𝑥 + 2 = 6
d) 𝑙𝑜𝑔9 𝑥 + 𝑙𝑜𝑔9 𝑥 = 3
2. Identify the transformation:
𝑦 = 2(𝑥 − 1)2 +10
Warm Up
Solve for x. Use properties when needed
a) 𝑙𝑜𝑔8 𝑥 + 1 = 3
b) −4 ∙ 25𝑥−6 = −64
Warm Up
Solve for x. Use properties when needed
c) 𝑙𝑜𝑔2 3𝑥 + 1 − 𝑙𝑜𝑔2 𝑥 + 2 = 6
Warm Up
Solve for x. Use properties when needed
d) 𝑙𝑜𝑔9 𝑥 + 𝑙𝑜𝑔9 𝑥 = 3
Warm Up
Identify the transformation:
𝑦 = 2(𝑥 − 1)2 +10
Homework Questions
Graphing Exponential Functions
𝑥
On your calculator, graph the
𝑦=𝑏
following equations:
If 𝑏 > 1 the graph is
𝑦 = 2𝑥
𝑥
increasing
1
(exponential growth)
𝑦=
2
If 0 < 𝑏 < 1 the graph
𝑥
𝑦=4
is
decreasing
𝑦 =.1𝑥
(exponential decay)
What do you notice about each graph?
Graphing Exponential Functions
On your calculator, graph the
equations:
𝑦 = 10𝑥
𝑦 = 10𝑥 − 5
𝑦 = 10𝑥+4
𝑦 = 10𝑥−6 + 3
Graphing Exponential Functions
𝒙−𝒉
𝒚=𝒃
+𝒌
Graphing Exponential Functions
On your calculator, graph the
equations:
𝑦 = 𝑙𝑜𝑔𝑥
𝑦 = log 𝑥 + 5
𝑦 = 𝑙𝑜𝑔𝑥 − 4
𝑦 = log 𝑥 − 3 + 2
Graphing Exponential Functions
𝒚 = 𝒍𝒐𝒈𝒃 𝒙 − 𝒉 + 𝐤
Features of Exponential and Log
Graphs
Asymptote: a line that a graph approaches
but does not cross
• Exponential functions: 𝑦 = 𝑏 𝑥−ℎ + 𝑘
– k is the horizontal asymptote
• Log Functions y = 𝑙𝑜𝑔𝑏 𝑥 − ℎ + k
– H is the vertical asymptote
Features of Exponential and Log
Graphs
End Behavior:
• What value is the function approaching
as x goes to infinity? To negative infinity?
As y goes to infinity and negative infinity?
BREAK
Identify the Transformation
For each graph, identify the transformation,
including the equation of the asymptote
𝑥+5
𝑦=3
−1
Increasing function
Left 5
Down 1
Horizontal asymptote at 𝑦 = −1
Identify the Transformation
For each graph, identify the transformation,
including the equation of the asymptote
𝑥−2
𝑦 = 1.5
+4
𝑦 = 4𝑥−3 + 6
𝑦 = 𝑙𝑜𝑔2 𝑥 − 7 + 5
𝑦 = 𝑙𝑜𝑔3 𝑥 + 9 − 1
𝑥+1
5) 𝑦 = 0.8
−7
1)
2)
3)
4)
QUIZ
AA4a and AA4b
You may use your notes as a reference
Homework
AA4 Practice Test
Sketching a Graph
Graph the equation 𝑦 =
2𝑥+2 − 1 by hand
1) Identify the
asymptote
2) Find the y-intercept
3) Identify the xintercept (if there is
one)
Sketching a Graph
Graph the equation 𝑦 =
𝑙𝑜𝑔4 𝑥 − 1 − 1 by hand
1) Identify the
asymptote
2) Find the y-intercept
(if there is one)
3) Find the x-intercept
Complete and put in the INBOX
Homework: