The language of functions
107P1^
4
Mappings
In mathematics, many (but not all) mappings can be expressed using algebra.
Here are some examples of mathematical mappings.
(a) Domain: integers Range
Objects Images
− 1 3
0 5
1 7
2 9
3 11
General rule: x 2 x + 5
(b) Domain: integers Range
Objects Images
1.9
2 2.1
2.33
2.52
3 2.99
π
General rule: Rounded whole numbers Unrounded numbers
(c) Domain: real numbers Range
Objects Images
0
45 0
90 0.707
135 1
180
General rule: x° sin x°
(d) Domain: quadratic Range
equations with real roots
Objects Images
x^2 − 4 x + 3 = 0 0
x^2 − x = 0 1
x^2 − 3 x + 2 = 0 2
3
General rule: ax^2 + bx + c = (^0) x bb ac
= a
––^2 – 4
2
(^) x bb ac
= a