1. PARENT GRAPH TOOLKIT Name: Lines x y x y -3 -2 -1 1 23 x y10
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

2. 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

3. 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

4. PARENT GRAPH TOOLKIT x y -3 -2 -1 1 2 3 x y Name: Reciprocal10 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

5. PARENT GRAPH TOOLKIT Name: Exponential x y -3 -2 -1 1 2 4 3 8 x y10
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

6. 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