With
TRANSFORMATIONS OF FUNCTIONS
| Variable | Replace With |
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| y | y - 2 | Vertical translation | Transfer the graph vertically 2 units up |
| y | y + 2 | Vertical translation | Transfer the graph vertically 2 units down |
| x | x - 3 | Horizontal translation | Transfer the graph horizontally 3 units right |
| x | x + 3 | Horizontal translation | Transfer the graph horizontally 3 units left |
| x | -x | Reflection in the y-axis | |
| y | -y | Reflection in the x-axis | |
| y |
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Vertical expansion | Expand the graph vertically by a factor 3 |
| y | 3y | Vertical compression | Compress the graph vertically by a factor 1/3 |
| x |
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Horizontal expansion | Expand the graph horizontally by a factor 2 |
| x | 3x | Horizontal compression | Compress the graph horizontally by a factor 1/3 |
TRANSFORMATIONS OF EXPONENTIAL FUNCTIONS
Example 1:
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Graph: Red: y = 2x Blue: y = (1/2)x
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Example 2:
Graph: y = 2x-2 – 3
Steps are given below:
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Step 1 y = 2x red
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Step 2 y = 2x-2 blue
Translate the graph 2 units to the right (replace x by (x-2))
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Step 3 y = 2x-2 – 3 green
Translate the graph 3 units down ((replace y by (y+3) |
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Example 3:
Graph: y = (-2)(1/3)x+4 + 2
Steps are given below:
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Step 1 y = 3x red |
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Step 2 y = (1/3)x
blue Reflect the graph in y axis |
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Step 3 3 = (1/3)x+4 green
Translate the graph 4 units to the left (replace x by (x+4)). |
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Step 4 y = 2(1/3)x+4 black
Expand the graph vertically by a factor of 2
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Step 5 y = -2(1/3)x+4
magenta Reflect the graph in x axis |
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Step 6 y = (-2)(1/3)x+4 + 2
brown Translate the graph 2 units up ((replace y by (y-2)
Equation of asymptote: x=2 Domain: all real values Range: y < 2
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