'Vertical shifts' diaporamas de présentation

Section 2.5

Section 2.5. Transformations of Functions. Overview. In this section we study how certain transformations of a function affect its graph. We will specifically look at: Shifting Reflecting Stretching. Vertical Shifting.

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Section 2.5 Transformation of Functions

Section 2.5 Transformation of Functions. Graphs of Common Functions. Reciprocal Function. Vertical Shifts. Vertical Shifts. Example. Use the graph of f(x)=|x| to obtain g(x)=|x|-2. Horizontal Shifts. Horizontal Shifts. Example. Use the graph of f(x)=x 2 to obtain g(x)=(x+1) 2.

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New York State Common Core Learning Standards

New York State Common Core Learning Standards. Mathematics. Presented by Joyce Bernstein East Williston UFSD Elaine Zseller, Ph.D. Nassau BOCES. Why Common Core State Standards?.

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100

Trig. Jeopardy!. 100. 100. 100. 100. 100. 200. 200. 200. 200. 200. 300. 300. 300. 300. 300. 400. 400. 400. 400. 400. 500. 500. 500. 500. 500. 100. Find a positive AND negative coterminal angle for -100 ?. Answer: 260 ? and -460 ? . 200.

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Chapter 1

Chapter 1 . 1-4 Shifting, reflecting and stretching graphs. objectives. The student will be able to: Recognize graphs of parent functions Use vertical and horizontal shifts and reflections to graph functions Use nonrigid transformations. Parent functions. What are parent functions?

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SECTION 1.5

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Turn homework into the box-staple together and make sure both names are on sheet!! Sckett

Turn homework into the box-staple together and make sure both names are on sheet!! Sckett. Transformation of Functions. Linear Function f(x) = x. The squaring function . The absolute value function . Absolute value- distance from zero for order of operations works like ( ).

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Practice with Quick Sketches

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Transformations : Shifting, Reflecting and Stretching Graphs

Transformations : Shifting, Reflecting and Stretching Graphs. GPS Algebra (MM1A1c) Graph transformations of parent functions. GPS Algebra Standards. MM1A1:

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y = csc X

y = csc X. Recall from the unit circle that csc ? = r/y. csc ? is undefined whenever y = 0. y = csc x is undefined at x = 0 , x = ? and x= 2 ?. Domain of Cosecant Function.

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y = sec x

y = sec x. Recall from the unit circle that: sec = r/x. sec is undefined whenever x = 0. Between 0 and 2 ?, y = sec x is undefined at x = ? /2 and x = 3 ? /2. Domain. Since sec x is undefined at ? /2, 3 ? /2, etc., the asymptotes appear at ? /2 + k ?. Range of Secant Function.

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y = sec x

y = sec x. Recall from the unit circle that: sec = r/x. sec is undefined whenever x = 0. Between 0 and 2 ?, y = sec x is undefined at x = ? /2 and x = 3 ? /2. Domain. Since sec x is undefined at ? /2, 3 ? /2, etc., the asymptotes appear at ? /2 + k ?. Range of Secant Function.

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Transformations of Functions

Transformations of Functions. Graphs of Common Functions. See Table 1.4, pg 184. Characteristics of Functions: Domain Range Intervals where its increasing, decreasing, or constant symmetry. y = f ( x ) + c. y = f ( x ). c. c. y = f ( x ). y = f ( x ) - c.

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Functions: Transformations of Graphs

Functions: Transformations of Graphs. Vertical Translation: The graph of f ( x ) + k appears as the graph of f ( x ) shifted up k units ( k > 0) or down k units ( k < 0). Example 1: Sketch the graphs of. 6. 5. 4. and on the same rectangular coordinate plane. 3. 2.

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Activity 2 - 4

Activity 2 - 4. Family of Functions. Objectives. Identify the effect of changes in the equation of a line on its graph Identify the effect of changes in the graph of a line on its equation

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Warm up

Warm up. Find 1. h(3) 2. -2h(4). Reflecting Graphs 8.3. Goal. We have talked about horizontal and vertical shifts, now we are going to FLIP the graph. . What do these look like?. Flipped over y-axis. Flipped over x-axis. We use Negative signs to flip:. Given a function y=f(x)

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Vertical shifts (up)

Vertical shifts (up). A familiar example:. y-values each increase by 3. Vertical shift up 3:. graph is shifted up 3 units. More vertical shifts (down). Original curve:. y-values each decrease by 5. Vertical shift down 5:. graph is shifted down 5 units. Horizontal shifts (right).

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AGENDA: PRE-CALCULUS HONORS. TUE. ODD DAY 93; 01/21/14 (3 rd 9-WEEK

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Chapter 7: Trigonometric Graphs 7.1: Graphs of the Sine, Cosine, and Tangent Functions

Chapter 7: Trigonometric Graphs 7.1: Graphs of the Sine, Cosine, and Tangent Functions. Essential Question: How do you graph a transformation of the sine, cosine, and tangent graphs?. 7.1: Graphs of Sin/Cos/Tan.

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