bellwork use a table of values to sketch the graph y

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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January 28, 2020

Transformations

1. Vertical/Horizontal Shifts

2. Vertical/Horizontal Reflections

3. Vertical/ Horizontal Shrinks and Stretches


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January 28, 2020

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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January 28, 2020

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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January 28, 2020

TransformationsHorizontal and Vertical Reflections

Flips a graph over x and y axis


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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January 28, 2020

TransformationsVertical Shrink and Stretch

Stretches and shrinks the graph vertically


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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January 28, 2020

f(cx)

TransformationsHorizontal Shrink and Stretch

Stretches and shrinks the graph horizontally


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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January 28, 2020

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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January 28, 2020

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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January 28, 2020

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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January 28, 2020

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:




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January 28, 2020

Transformations

Write an equation that describes the graph.


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January 28, 2020

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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January 28, 2020

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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January 28, 2020

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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January 28, 2020

Transformation Practice


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January 28, 2020

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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January 28, 2020

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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January 28, 2020

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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January 28, 2020

Transformations

f(x)

f(x)


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January 28, 2020

bellwork use a table of values to sketch the graph y

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