Relations and Functions Equations and Graphs Domain and Range

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 x

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 x

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

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

Parabola 3) y = x 2 D: 7) x = y 2 D: 11) y = x 2 – 4 D: x | y x | y x | y (-1, )R: (1, ) R: (-1, ) R: (0, ) (0, ) (0, ) (1, )F ? (1, ) F ? (1, ) F? y x y x 5 5 y x 5 5

Parabola 3) y = x 2 D: 7) x = y 2 D: 11) y = x 2 – 4 D: x | y Ʀ x | 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? Yes No Yes y x y x 5 5 y x 5 5

Parabola 3) y = x 2 D: 7) x = y 2 D: 11) y = x 2 – 4 D: x | y Ʀ x | 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? Yes No Yes y x y x 5 5 y x 5 5

Square Root 4) y = √ x x | yD: (0, 0)[0, ∞) (1, 1)R: (4, 2)[0, ∞) F ? Yes y x

Square Root 4) y = √ x x | yD: (0, 0)[0, ∞) (1, 1)R: (4, 2)[0, ∞) F ? Yes y x

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? y x y x 5 5 y x 5 5

Absolute Value 5) y = |x| D: 8) x = |y| D: 10) y=|x|+6 D: x | y Ʀ x | 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? Yes No Yes y x y x 5 5 y x 5 5

Absolute Value 5) y = |x| D: 8) x = |y| D: 10) y=|x|+6 D: x | y Ʀ x | 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? Yes No Yes y x y x 5 5 y x 5 5