11 - 1 : Students will be able to determine the key features of square root functions including: zeros, y-intercepts, end points, maxima, minima, domain, range, and end behavior 11 - 2 : Students will be able to graph absolute value functions and describe their transformations including: reflections across the x-axis, reflections across the y-axis, vertical stretch and compression, horizontal stretch and compression, horizontal shifts (left and right), and vertical shifts (up and down)
Examples
Key Features
Transformations
Graph the Square Root Function 11-1: Determine all Key Features of the function. 11-2: Describe all Transfomrations
Outcome 11-1 & 11-2
Graph the Square Root Function 11-1: Determine all Key Features of the function. 11-2: Describe all Transfomrations
Outcome 11-1 & 11-2
Graph the Square Root Function 11-1: Determine all Key Features of the function. 11-2: Describe all Transfomrations
Outcome 11-1 & 11-2
Zeros: noney-intercept: (0, 4) End Point: (0, 4) Maximum / Minimum: Min (0, 4) Domain: (-∞, 0] Range: [4, ∞) End Behavior: As x → -∞, f(x) → ∞ As x → 0, f(x) → 4
1. Reflection: Reflection across y-axis 2. Stretch / Compression: Vertical Stretch (2) No Horizontal S/C 3. Horizontal Shift: No Horizontal Shift 4. Vertical Shift: Vertical Shift Up (4)
Zeros: noney-intercept: none End Point: (3, -3) Maximum / Minimum: Max (3, -3) Domain: [3, ∞) Range: (-∞, -3] End Behavior: As x → 3, f(x) → -3 As x → ∞, f(x) → -∞
1. Reflection: Reflection across x-axis 2. Stretch / Compression: No Vertical S/C No Horizontal S/C 3. Horizontal Shift: Horizontal Shift Right (3) 4. Vertical Shift: Vertical Shift Down (3)
Zeros: (-0.9, 0)y-intercept: (0, 2) End Point: (-2, -6) Maximum / Minimum: Min (-2, -6) Domain: [-2, ∞) Range: [-6, ∞) End Behavior: As x → -2, f(x) → -6 As x → ∞, f(x) → ∞
Zeros: (9.5, 0)y-intercept: none End Point: (3, 5) Maximum / Minimum: Max (3, 5) Domain: [3, ∞) Range: (-∞, 5] End Behavior: As x → 3, f(x) → 5 As x → ∞, f(x) → -∞
Zeros: (4.5, 0)y-intercept: none End Point: (4, 1) Maximum / Minimum: Max (4, 1) Domain: [4, ∞) Range: (-∞, 1] End Behavior: As x → 4, f(x) → 1 As x → ∞, f(x) → -∞
Zeros: N/Ay-intercept: (0, -2.5) End Point: (2, -3) Maximum / Minimum: Min (2, -3) Domain: (-∞, 2] Range: [-3, ∞) End Behavior: As x → -∞, f(x) → ∞ As x → 2, f(x) → -3
1. Reflection: Reflection across 2. Stretch / Compression: Vertical Stretch ( Horizontal Compression 3. Horizontal Shift: Horizontal Shift ( 4. Vertical Shift: Vertical Shift Up ()
1. Reflection: Reflection across x-axis 2. Stretch / Compression: Vertical Stretch (2) Horizontal Stretch (1/2) 3. Horizontal Shift: Horizontal Shift Right (4) 4. Vertical Shift: Vertical Shift Up (1)
1. Reflection: Reflection across x-axis 2. Stretch / Compression: Vertical Stretch (2) No Horizontal S/C 3. Horizontal Shift: Horizontal Shift Right (3) 4. Vertical Shift: Vertical Shift Up (5)
1. Reflection: No Reflection 2. Stretch / Compression: Vertical Stretch (4) Horizontal Compression (2) 3. Horizontal Shift: Horizontal Shift Left (2) 4. Vertical Shift: Vertical Shift Down (6)
Radical Functions - Graphing Square Roots
Kevin Helms
Created on October 10, 2025
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Transcript
11 - 1 : Students will be able to determine the key features of square root functions including: zeros, y-intercepts, end points, maxima, minima, domain, range, and end behavior 11 - 2 : Students will be able to graph absolute value functions and describe their transformations including: reflections across the x-axis, reflections across the y-axis, vertical stretch and compression, horizontal stretch and compression, horizontal shifts (left and right), and vertical shifts (up and down)
Examples
Key Features
Transformations
Graph the Square Root Function 11-1: Determine all Key Features of the function. 11-2: Describe all Transfomrations
Outcome 11-1 & 11-2
Graph the Square Root Function 11-1: Determine all Key Features of the function. 11-2: Describe all Transfomrations
Outcome 11-1 & 11-2
Graph the Square Root Function 11-1: Determine all Key Features of the function. 11-2: Describe all Transfomrations
Outcome 11-1 & 11-2
Zeros: noney-intercept: (0, 4) End Point: (0, 4) Maximum / Minimum: Min (0, 4) Domain: (-∞, 0] Range: [4, ∞) End Behavior: As x → -∞, f(x) → ∞ As x → 0, f(x) → 4
1. Reflection: Reflection across y-axis 2. Stretch / Compression: Vertical Stretch (2) No Horizontal S/C 3. Horizontal Shift: No Horizontal Shift 4. Vertical Shift: Vertical Shift Up (4)
Zeros: noney-intercept: none End Point: (3, -3) Maximum / Minimum: Max (3, -3) Domain: [3, ∞) Range: (-∞, -3] End Behavior: As x → 3, f(x) → -3 As x → ∞, f(x) → -∞
1. Reflection: Reflection across x-axis 2. Stretch / Compression: No Vertical S/C No Horizontal S/C 3. Horizontal Shift: Horizontal Shift Right (3) 4. Vertical Shift: Vertical Shift Down (3)
Zeros: (-0.9, 0)y-intercept: (0, 2) End Point: (-2, -6) Maximum / Minimum: Min (-2, -6) Domain: [-2, ∞) Range: [-6, ∞) End Behavior: As x → -2, f(x) → -6 As x → ∞, f(x) → ∞
Zeros: (9.5, 0)y-intercept: none End Point: (3, 5) Maximum / Minimum: Max (3, 5) Domain: [3, ∞) Range: (-∞, 5] End Behavior: As x → 3, f(x) → 5 As x → ∞, f(x) → -∞
Zeros: (4.5, 0)y-intercept: none End Point: (4, 1) Maximum / Minimum: Max (4, 1) Domain: [4, ∞) Range: (-∞, 1] End Behavior: As x → 4, f(x) → 1 As x → ∞, f(x) → -∞
Zeros: N/Ay-intercept: (0, -2.5) End Point: (2, -3) Maximum / Minimum: Min (2, -3) Domain: (-∞, 2] Range: [-3, ∞) End Behavior: As x → -∞, f(x) → ∞ As x → 2, f(x) → -3
1. Reflection: Reflection across 2. Stretch / Compression: Vertical Stretch ( Horizontal Compression 3. Horizontal Shift: Horizontal Shift ( 4. Vertical Shift: Vertical Shift Up ()
1. Reflection: Reflection across x-axis 2. Stretch / Compression: Vertical Stretch (2) Horizontal Stretch (1/2) 3. Horizontal Shift: Horizontal Shift Right (4) 4. Vertical Shift: Vertical Shift Up (1)
1. Reflection: Reflection across x-axis 2. Stretch / Compression: Vertical Stretch (2) No Horizontal S/C 3. Horizontal Shift: Horizontal Shift Right (3) 4. Vertical Shift: Vertical Shift Up (5)
1. Reflection: No Reflection 2. Stretch / Compression: Vertical Stretch (4) Horizontal Compression (2) 3. Horizontal Shift: Horizontal Shift Left (2) 4. Vertical Shift: Vertical Shift Down (6)