PreCalculus Chapter 1 Section 6

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Presentation transcript:

PreCalculus Chapter 1 Section 6 Graphical Transformations

Transformations In this section we will look at both rigid transformations and non- rigid transformations. Rigid Transformations: leave the size and shape of the graph unchanged. These include translations, reflections, or any combination of these. Non-rigid Transformations: distort the shape of the graph. These include horizontal & vertical stretches and shrinks.

Translations Let c be a positive real number. Then the following transformations result in translations of the graph. Horizontal Translations y = f(x – c) a translation to the right by c units. y = f(x + c) a translation to the left by c units. Vertical Translations y = f(x) + c a translation up by c units y = f(x) – c a translation down by c units

Reflections Across the x-axis: y = - f(x) Across the y-axis: y = f(-x) See diagram on page 141

Graphing Absolute Value Compositions Given the graph of y = f(x), The graph of y = ∣f(x)∣ can be obtained by making all y-values positive and reflecting the portion of the graph below the x-axis to the top-side of the x-axis. The graph of y = f(∣x∣) can be obtained by all x-values positive and reflecting the portion of the graph left of the y-axis to the right-side of the y-axis. See exploration #2 on page 143.

Vertical & Horizontal Stretches and Shrinks Let c be a positive real number. Horizontal Stretches & Shrinks: y = f (c x) a stretch by a factor 1/c if c < 1 a shrink by a factor of 1/c if c > 1 Vertical Stretches & Shrinks: y = c f(x) a stretch by a factor of c if c > 1 a shrink by a factor of c if c < 1 See exploration # 3 on page 144.

Homework # 3 – 54 by multiples of 3 on pages 147 – 148.