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Relations and Functions

Relations and Functions. Equations and Graphs Domain and Range. y. 5. x. -5. -5. 5. Lines. Ax + By = C Standard Form y = mx + b Slope-Intercept Form 9) 5x – 2 y = 10 ( Standard Form) 5x – 2 y = 10 -2y = -5x + 10 y = 5/2 x – 5 ( Slope-Intercept Form). y. 5. x. -5.

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Relations and Functions

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  1. Relations and Functions Equations and Graphs Domain and Range

  2. y 5 x -5 -5 5 Lines Ax + By = C Standard Form y = mx + b Slope-Intercept Form 9) 5x – 2 y = 10 (Standard Form) 5x – 2 y = 10 -2y = -5x + 10 y = 5/2 x – 5 (Slope-Intercept Form)

  3. y 5 x -5 -5 5 Lines Ax + By = C Standard Form y = mx + b Slope-Intercept Form 9) 5x – 2 y = 10 (Standard Form) 5x – 2 y = 10 -2y = -5x + 10 y = 5/2 x – 5 (Slope-Intercept Form)

  4. y y y y 5 5 5 5 x x x x -5 -5 -5 -5 -5 -5 -5 -5 5 5 5 5 Slope Four Types of Slopes Positive, Negative, No Slope, 0 Slope Slants up L to RVerticalHorizontal 1) y = 2x – 1 2) 2x – 1 = 5 6) y – 2 = 7 D: D: D: Ʀ {3} Ʀ R: R: R: Ʀ Ʀ {9} F ? F ? F ? Yes No Yes

  5. y y y y 5 5 5 5 x x x x -5 -5 -5 -5 -5 -5 -5 -5 5 5 5 5 Slope Four Types of Slopes Positive, Negative, No Slope, 0 Slope Slants up L to RVerticalHorizontal 1) y = 2x – 1 2) 2x – 1 = 5 6) y – 2 = 7 D: D: D: Ʀ {3} Ʀ R: R: R: Ʀ Ʀ {9} F ? F ? F ? Yes No Yes

  6. y y y 5 5 5 x x x -5 -5 -5 -5 -5 -5 5 5 5 Parabola 3) y = x2 D: 7) x = y2 D: 11) y = x2 – 4 D: x | y x | y x | y (-1, ) R: (1, ) R: (-1, ) R: (0, ) (0, ) (0, ) (1, ) F ? (1, ) F ? (1 , ) F?

  7. y y y 5 5 5 x x x -5 -5 -5 -5 -5 -5 5 5 5 Parabola 3) y = x2 D: 7) x = y2 D: 11) y = x2 – 4 D: x | y Ʀx | y [0, ∞)x | y Ʀ (-1, 1) R: (1, -1) R: (-1, -3) R: (0, 0) [0, ∞) (0, 0 ) Ʀ (0, -4)[-4, ∞) (1, 1) F ? (1, 1 ) F ? (1 , -3) F? YesNo Yes

  8. y y y 5 5 5 x x x -5 -5 -5 -5 -5 -5 5 5 5 Parabola 3) y = x2 D: 7) x = y2 D: 11) y = x2 – 4 D: x | y Ʀx | y [0, ∞)x | y Ʀ (-1, 1) R: (1, -1) R: (-1, -3) R: (0, 0) [0, ∞) (0, 0 ) Ʀ (0, -4)[-4, ∞) (1, 1) F ? (1, 1 ) F ? (1 , -3) F? YesNo Yes

  9. y 5 x -5 -5 5 Square Root 4) y = √ x x | y D: (0, 0) [0, ∞) (1, 1) R: (4, 2) [0, ∞) F ? Yes

  10. y 5 x -5 -5 5 Square Root 4) y = √ x x | y D: (0, 0) [0, ∞) (1, 1) R: (4, 2) [0, ∞) F ? Yes

  11. y y y 5 5 5 x x x -5 -5 -5 -5 -5 -5 5 5 5 Absolute Value 5) y = |x| D: 8) x = |y| D: 10) y=|x|+6 D: x | y x | y x | y (-1, ) R: ( , -1) R: (-1, ) R: (0, )( , 0 ) (0, ) (1, ) F ? ( , 1 ) F ? (1 , ) F?

  12. y y y 5 5 5 x x x -5 -5 -5 -5 -5 -5 5 5 5 Absolute Value 5) y = |x| D: 8) x = |y| D: 10) y=|x|+6 D: x | y Ʀx | y [0, ∞)x | y Ʀ (-1, 1) R: (1, -1) R: (-1, 7) R: (0, 0) [0, ∞) (0, 0 ) Ʀ (0, 6) [6, ∞) (1, 1) F ? (1, 1 ) F ? (1 , 7) F? YesNo Yes

  13. y y y 5 5 5 x x x -5 -5 -5 -5 -5 -5 5 5 5 Absolute Value 5) y = |x| D: 8) x = |y| D: 10) y=|x|+6 D: x | y Ʀx | y [0, ∞)x | y Ʀ (-1, 1) R: (1, -1) R: (-1, 7) R: (0, 0) [0, ∞) (0, 0 ) Ʀ (0, 6) [6, ∞) (1, 1) F ? (1, 1 ) F ? (1 , 7) F? YesNo Yes

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