

Graphing logarithmic functions with transformations
Presentation
•
Mathematics
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9th - 12th Grade
•
Practice Problem
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Medium
Standards-aligned
Beth Knott
Used 37+ times
FREE Resource
8 Slides • 6 Questions
1
Graphing logarithmic functions with transformations

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y=logbx parent function
points: (b1, −1), (1, 0), (b,1)
asymptote: x = 0
The graph to the right shows the parent function y=log2(x)
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Transformations
Follow your order of operations
1st: parenthesis - follow order of operations inside parenthesis
2nd: multiplication and division
3rd: addition and subtraction
Asymptote only moves with shift left/right
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Graph
y=−log2(x+4)Parent function points: (21, −1),(1,0), (2,1)
1st transformation: shift left 4 x -4
2nd transformation: reflect over x axis y(-1)
New rule: (x - 4, -1y) don't forget to move asymptote!
(-3.5, 1), (-3, 0), (-2, -1) asymptote: x = -4
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y=−log2(x+4)
(-3.5, 1), (-3,0), (-2, -1)
asymptote: x = -4
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Multiple Choice
y = log2(−x)+3 has the following parent points: (21,−1), (1,0), (2,1) What would happen after the first transformation?
Reflect over the x axis: y(-1)
Reflect over the y axis: x(-1)
Shift up 3: x + 3
Shift up 3: y + 3
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Multiple Choice
y = log2(−x)+3 has the following parent points: (21,−1), (1,0), (2,1) What would happen after the second transformation?
Reflect over the x axis: y(-1)
Reflect of the y axis: x(-1)
Shift up 3: x + 3
Shift up 3: y + 3
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Multiple Choice
y=log2(−x)+3 has parent points: (21,−1), (1,0), (2, 1) The transformations gave you: (-1x, y +3). What would be the transformed points?
(−21,2),(−1,3), (−2,4)
(2.5,−1),(2,0), (0,1)
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Multiple Choice
y=−2log3(x+1) has parent points: (31, −1), (1, 0), (3,1) What is the 1st transformation?
reflect over x axis and vertical stretch: -2(x)
reflect over x axis and vertical stretch: -2(y)
shift left 1: x - 1
shift left 1: y - 1
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Multiple Choice
y=−2log3(x+1) has parent points: (31, −1), (1, 0), (3,1) What is the 2nd transformation?
reflect over x axis and vertical stretch: -2(x)
reflect over x axis and vertical stretch: -2(y)
shift left 1: x - 1
shift left 1: y - 1
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Multiple Choice
y=−2log3(x+1) has parent points: (31, −1), (1, 0), (3,1) Transformations gave the rule (x - 1, -2y). What are the points of the new function?
(−32,2),(0,0),(2,−2)
(−32,−2),(−2,−1), (−6,0)
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y=−2log3(x+1)
(−32,2),(0,0),(2,−2)
asymptote: x = -1
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Homework in Khan Academy
1. Graphs of logarithmic functions due tomorrow 11:59 pm
Test on Monday/Tuesday
Graphing logarithmic functions with transformations

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