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P.3: Part 2 Functions and their Graphs
Transformations on Parent Functions: y = f(x): Parent Functions y = f(x – c) y = f(x + c) y = f(x) – c y = f(x) + c y = -f(x) y = f(-x) y = -f(-x) y = df(x) y = f(dx)
Describe what would happen to the parent function and sketch graphs of each: f(x) = 3(x + 2) 2 – 1
Describe what would happen to the parent function and sketch graphs of each: f(x) = -3sin(x + π/2) + 2
Composite Functions: f(x) = x 2 – 1, g(x) = cos x Find f ° gFind g ° f Give the domain of each composite function.
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EQ: How can transformations effect the graph a parent function? I will describe how transformations effect the graph of a parent function.
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Write equation or Describe Transformation. Write the effect on the graph of the parent function down 1 unit1 2 3 Stretch by a factor of 2 right 1 unit.
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This is the graph of y = sin x o The maximum value of sin x o is 1 The minimum value of sin x o is -1 Amplitude = 1 We say the period of y = sin x o is.
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#1 Find the quadrant in which lies.. #1 Find the quadrant in which lies.
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1 What you will learn How to graph a basic sin and cos function.
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Warm Up 1. Determine whether each function is one-to-one. a) y = 2x 3 – 3x b) y = 6x +14 c) y = 5x 2 – x + 3 d) 2. Find the inverse of.
Sketching sin & cos graphs Example 1 Sketch one period of y = 3 sinx + 2 Vert:Average = 2 Amplitude = 3 Range y [-1, 5] Horiz:Period = 2π Ref Pt: average.
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