PARENT GRAPH TOOLKIT Name: Lines x y x y -3 -2 -1 1 23 x y 10 Name: Lines x y x y -3 -2 -1 1 23 x y 8 Parent Equation: y = x 6 4 Description of Locator: 2 (0, 0) x y–intercept (0, y) –4 –2 2 4 –2 General Equation: –4 y = mx + b –6 –8 Properties: –10 (steepness) Domain: Range: {x| x  R} {y| y  R} b = y–intercept

parabolas opening down PARENT GRAPH TOOLKIT y 10 Name: Parabolas x y x y -3 -2 -1 1 23 9 4 49 (3, 9) 8 Parent Equation: y = x2 6 4 (2, 4) Description of Locator: 2 (1, 1) x vertex (h, k) –4 –2 2 4 (0, 0) –2 General Equation: –4 y = a(x – h)2 + k –6 Properties: –8 Open up or down horizontal shift –10 Domain: Range: y =+/- a(x – h)2 + k parabolas opening up {x| x  R} {y| k ≤ y < } Wider or narrower {y| –< y ≤ k} vertical shift parabolas opening down

PARENT GRAPH TOOLKIT Name: Cubics x y x y -2 -1 1 2 -8 8 (2, 8) 10 Name: Cubics x y x y -2 -1 1 2 -8 8 8 (2, 8) Parent Equation: y = x3 6 4 Description of Locator: 2 (1, 1) (0, 0) x inflection point (h, k) –4 –2 2 4 (–1, –1) –2 General Equation: –4 y = a(x – h)3 + k –6 (–2, –8) –8 Properties: –10 flip horizontal shift Domain: Range: y = +/- a(x – h)3 + k {x| x  R} {y| y  R} Wider or narrower vertical shift

PARENT GRAPH TOOLKIT x y -3 -2 -1 1 2 3 x y Name: Reciprocal 10 x y -3 -2 -1 1 2 3 x y Name: Reciprocal 8 Parent Equation: 6 4 Description of Locator: 2 (1, 1) y = 0 (0, 0) x intersection of asymptotes (h, k) –4 –2 2 4 (–1, –1) –2 General Equation: –4 –6 –8 Properties: –10 x = 0 vertical asymptote Domain: Range: x = h {x| x  h} {y| y  k} horizontal asymptote y = k

PARENT GRAPH TOOLKIT Name: Exponential x y -3 -2 -1 1 2 4 3 8 x y 10 Name: Exponential x y -3 -2 -1 1 2 4 3 8 x y (3, 8) 8 Parent Equation: y = 2x 6 4 (2, 4) Description of Locator: (1, 2) 2 x Point that is 1 unit above the asymptote (0, 1) (h, k + 1) –4 –2 2 4 y = 0 –2 General Equation: –4 y = a  b(x – h) + k –6 –8 Properties: –10 y = a  b(x – h) + k Domain: Range: horizontal shift vertical shift {x| x  R} {y| k < y < } Horizontal asymptote y = k

PARENT GRAPH TOOLKIT Name: Absolute Value x y -3 -2 -1 1 2 3 x y PG – 114 PARENT GRAPH TOOLKIT y x 2 4 –2 –4 8 6 10 –6 –8 –10 Name: Absolute Value x y -3 -2 -1 1 2 3 x y Parent Equation: y = | x | Description of Locator: (–1, 1) (1, 1) vertex (h, k) (0, 0) General Equation: y = a|x – h| + k Properties: open up or down horizontal shift Domain: Range: y = +/- a|x – h| + k {x| x  R} {y| k ≤ y < } Wider or narrower (-, ) [k, ) vertical shift