Type of Function
Picture
Linear
Characteristics
Parent Function: y=x
Transformation :2units up
Domain: (−∞ , ∞ )∧Range :(−∞, ∞ )
y−Intercept =2
Zeros :(−2,0)
No Symmetry , Neither E ven nor Odd
f (x) →−∞ as x →−∞ ; f (x )→ ∞ as x → ∞
Increasing¿ (−∞ , ∞)
2
Quadratic
Exponential
Parent Function: y=x
Transformation :2units down
Domain : (−∞ , ∞ )∧Range : ¿
y−Intercept =−2
Zeros : (− √2 , 0 ) , ( √ 2 , 0 )
Symmetric with y−axis , Even
f (x) →∞ as x →−∞ ; f (x )→ ∞ as x → ∞
Increasing¿ ( 0 , ∞ ) , Decreasing ¿(−∞ , 0)
Parent Function: y=e x
Transformation :2units up
Domain: (−∞ , ∞ )∧Range :(−2, ∞ )
y−Intercept =3
¿
Zeros :¿
No Symmetr y , Even
f (x) →2 as x →−∞ ; f (x )→ ∞ as x → ∞
Increasing¿ (−∞ , ∞ )
1
x2
Transformation :2units ¿
Domain: (−∞ , 2 ) ∪(2, ∞)∧Range :(0 , ∞)
1
y−Intercept =
4
¿
Zeros :¿
No Symmetry , Neither E ven nor Odd
f ( x)→0 as x →−∞ ; f ( x)→0 as x → ∞
Increasing¿ (−∞, 2 ) , Decreasing ¿ (2, ∞)
Parent Function: y=
Rational
PRECALCULUS Part 1 – Unit 3 Assignment:
Functions in the Real World
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