Bellwork Use a table of values to sketch the graph y ...
Transcript of Bellwork Use a table of values to sketch the graph y ...
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Transformations.notebook
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January 28, 2020
Bellwork
Use a table of values to sketch the graph
y = | x 5| + 1
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Transformations.notebook
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Transformations
1. Vertical/Horizontal Shifts
2. Vertical/Horizontal Reflections
3. Vertical/ Horizontal Shrinks and Stretches
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Transformations
Vertical Shifts
Moving a Graph Up or Down
Given the parent function, f(x)...
Shifts f(x) up c units
Shifts f(x) down c units
f(x) + c f(x) c
x f(x) = x f(x) = x + 2 f(x) = x 1
2
1012
Adds and subtracts c from y
To find transformed point:
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Transformations
Horizontal Shifts
Moving a Graph right or left
Given the parent function, f(x)... x f(x) = x2 f(x) = (x + 2)2 f(x) = (x 1)2
2 1012
Adds and subtracts c from x
Shifts f(x) right c units
Shifts f(x) left c units
f(x c)
f(x + c)
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TransformationsHorizontal and Vertical Reflections
Flips a graph over x and y axis
Given the parent function, f(x)...
x f(x) = 2x f(x) = 2x f(x) = 2 x
2 1012
Multiplies y by a negative
Multiplies x by a negative
Reflects f(x) over xaxis
Reflects f(x) over yaxis
f(x)
f( x)
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TransformationsVertical Shrink and Stretch
Stretches and shrinks the graph vertically
Given the parent function, f(x)...
x f(x) = |x| f(x) = 2|x| f(x) = 1/2|x|
2 1012
Multiplies y by c
c f(x) .
Vertically stretches f(x)
Vertically shrinks f(x)
c f(x) .c > 1
0 < c < 1
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f(cx)
TransformationsHorizontal Shrink and Stretch
Stretches and shrinks the graph horizontally
Given the parent function, f(x)...
x f(x) = x3 f(x) = (2x)3 f(x) = (1/2x)3
2 1012
Multiplies y by c
Horizontally stretches f(x)
Horizontally shrinks f(x)
f(cx) c > 1
0 < c < 1
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Transformations
The point (1,1) is on f(x). After a series of 3 transformations, (1,1) has been moved to (2, 7). Write a functions g(x) that represents he transformation of f(x).
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Transformations
Write a function g whose graph represents the indicated transformation of the graph of f.
1. f(x) = |3x|; translated 2 units left.
2. f(x) = (x + 9)2 1; translated 6 units down.
3. f(x) = 5x; vertical shrink by a factor of 1/5.
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TransformationsPractice: Sketch the graphs after the transformations of the quadratic parent function.
1. f(x 3) + 1
Parent Function: f(x) =
2. f(2x) + 2
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TransformationsPractice Give the name of the parent function and
describe the transformation represented.
1. g(x) = |x2|+ 3
2. f(x) =
3. h(x) = (x5)2+ 1
13x + 6
Parent Function: Transformations:
Parent Function: Transformations:
Parent Function: Transformations:
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Transformations
Write an equation that describes the graph.
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Transformations
The ordered pair (1,2) is on the graph f(x). Give the resulting ordered pair after the transformation of f(x + 3) 1
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Transformations
The ordered pair (9,3) is on the graph f(x). Give the resulting ordered pair after the transformation of 2f(x + 1) 3.
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TransformationsGraph each of the following transformations of the function graphed below.A. 2b(x) B. 2/3b(x) C. b(x)
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Transformation Practice
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Transformations
Talk to someone not in your group and find out their 1 song that they just can't help but sing along to.
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Transformations
Match each of the graph cards with its corresponding equation card and description.
Make sure you consult each person in your group before matching.
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Transformations
On the first graph, graph any function.
Rules:
1) can't be a parent function or a transformation of a parent function
2) have at least 5 points that are easy to see
3) Be sure to put end points or arrows
4) Does not have to be straight lines
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Transformations
f(x)
f(x)
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