Absolute Value Functions - Graphing

ABSOLUTE VALUE key features & transformations

OUTCOMES

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12 - 1 : Students will be able to determine the key features of absolute value functions including: zeros, y-intercepts, vertex, maximum or minimum, axis of symmetry, domain and range, and end behavior 12 - 2 : Students will be able to graph absolute value functions and describe their transformations including: reflections across the x-axis, vertical stretch and compression, horizontal shifts (left and right), and vertical shifts (up and down).

PRACTICE

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OUTCOMES

Transformations

Key Features

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Key Features

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Transformations

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845 x ...

NOTES

845 x ...

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NOTES

Advanced

Intermediate

Basic

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Outcome 12-1 & 12-2

Basic

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Graph the Absolute Value Function. 12-1: Determine the key features of g(x) 12-2: Describe the transformations of g(x)

PRACTICE

Outcome 12-1 & 12-2

Graph the Absolute Value Function. 12-1: Determine the key features of g(x) 12-2: Describe the transformations of g(x)

Intermediate

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PRACTICE

Graph the Absolute Value Function. 12-1: Determine the key features of g(x) 12-2: Describe the transformations of g(x)

Outcome 12-1 & 12-2

Advanced

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PRACTICE

1. Reflection: No reflection 2. Stretch / Compression: Vertical Stretch (2) 3. Horizontal Shift: No Horizontal Shift 4. Vertical Shift: Vertical Shift Up (4)

Zeros: (-2.5, 0), (0.5, 0)y-intercept: (0, -2) Vertex: (-1, -6) Maximum or Minimum: Min Axis of Symmetry: x = -1 Domain: (-∞, ∞) Range: [-6, ∞) End Behavior: As x → ∞, f(x) → ∞ As x → -∞, f(x) → ∞

1. Reflection: Reflection Across the x-axis 2. Stretch / Compression: No Stretch or Compression 3. Horizontal Shift: Horizontal Shift Right (3) 4. Vertical Shift: No Vertical Shift

Zeros: (3, 0)y-intercept: (0, -3) Vertex: (3, 0) Maximum or Minimum: Max Axis of Symmetry: x = 3 Domain: (-∞, ∞) Range: (-∞, 0] End Behavior: As x → ∞, f(x) → -∞ As x → -∞, f(x) → -∞

1. Reflection: No reflection 2. Stretch / Compression: Vertical Stretch (4) 3. Horizontal Shift: Horizontal Shift Left (1) 4. Vertical Shift: Vertical Shift Down (6)

1. Reflection: No reflection 2. Stretch / Compression: Vertical Compression (1/2) 3. Horizontal Shift: Horizontal Shift Left (4) 4. Vertical Shift: Vertical Shift Down (3)

1. Reflection: Reflection across the x-axis 2. Stretch / Compression: Vertical Stretch (2) 3. Horizontal Shift: Horizontal Shift Right (3) 4. Vertical Shift: No Vertical Shift

Zeros: Noney-intercept: (0, 4) Vertex: (0, 4) Maximum or Minimum: Min Axis of Symmetry: x = 0 Domain: (-∞, ∞) Range: [4, ∞) End Behavior: As x → ∞, f(x) → ∞ As x → -∞, f(x) → ∞

Zeros: (-10, 0), (2, 0)y-intercept: (0, -1) Vertex: (-4, -3) Maximum or Minimum: Min Axis of Symmetry: x = -4 Domain: (-∞, ∞) Range: [-3, ∞) End Behavior: As x → ∞, f(x) → ∞ As x → -∞, f(x) → ∞

Zeros: (2.5, 0), (3.5, 0)y-intercept: (0, -5) Vertex: (3, 1) Maximum or Minimum: Max Axis of Symmetry: x = 3 Domain: (-∞, ∞) Range: (-∞, 1] End Behavior: As x → ∞, f(x) → -∞ As x → -∞, f(x) → -∞

1. Reflection: Reflection Across the x-axis 2. Stretch / Compression: Vertical Stretch (2) 3. Horizontal Shift: Horizontal Shift Right (3) 4. Vertical Shift: Vertical Shift Up (1)

Zeros: (3, 0)y-intercept: (0, -6) Vertex: (3, 0) Maximum or Minimum: Max Axis of Symmetry: x = 3 Domain: (-∞, ∞) Range: (-∞, 0] End Behavior: As x → ∞, f(x) → -∞ As x → -∞, f(x) → -∞