Factoring with common tropes
x2+8x+15
(x+3)(x+5)
y=(x+6)2 - 4
(-6, -4)
y = x2 + 34x - 90
x → +∞, y → +∞ ;
x → -∞, y → +∞
x2 + 4x + 3 = 0
{−1, −3}
What is the domain for
y = x2
(-∞, ∞) or {x ∈ R}
3p2 − 2 p − 5
(3p − 5)( p + 1)
y = 2(x + 8)2 + 6
(-8, 6)
y = 13x5 + x3 - 23x2 + 2
x → +∞, y → +∞ ;
x → -∞, y → -∞
2x2 − 3x − 5 = 0
{ 5/2 , −1}
What is the Domain and range for
y = -x4 + 6
Domain = (-∞,∞) or {x ∈ R}
Range = (-∞, 6] or {y ∈ R: y≤ 6}
5n2 + 19n + 12
(5n + 4)(n + 3)
y = 2x2 + 4x +5
(-1, 3)
y = (3x + 2) / (x2 -5x -6)
x → +∞, y → 0 ;
x → -∞, y → 0
(this was an example from the textbook -6.1)
9n2 = 4 + 7n
{ (7 + sqrt(193) )/18 , (7 − sqrt(193))/ 18 }
What is the domain and range for
y = x15 + 15
Domain = (-∞, ∞) or {x ∈ R}
Range = (-∞, ∞) or {y ∈ R}
54x3-128
2(3x-4)(9x2+12x+16)
y = 4x2+56x + 188
(-7,-8)
y = (-x6 + 6x2 + 4x) / (3x5 + x4 - 8)
x → +∞, y → -∞ ;
x → -∞, y → +∞
8n2 + 4n − 16 = −n2
{ (−2 + 2 sqrt(37) )/9 , (−2 − 2 sqrt(37))/ 9 }
What is the domain for
y = 1 / (x2 -144)
(-∞,-12)⋃(-12,12)⋃(12,∞) or {x ∈ R: x≠12, -12}
2x4 − 2x3 − 7𝑥2+ 7𝑥
x(2x2-7)(x-1)
y = (5x-7)(x-1)
(1.2, -0.2) or (⁶⁄₅, -⅕)
y = -5 (x+3)(x-5) / 63(x-2)(x+6)
x → +∞, y → ⁻⁵⁄₆₃ ;
x → -∞, y → ⁻⁵⁄₆₃
2m2 − 7m − 13 = −10
{ (7 + sqrt(73))/4 , (7 − sqrt(73))/4 }
What is the domain and Range for
y = (3x2-27) / (x+3)(x-3)
Domain (-∞,-3)⋃(-3,3)⋃(3,∞) or {x ∈ R: x≠-3, 3}
Range [3] or {y=3}