Page 9 - Spotlight A+ SPM Additional Mathematics Form 4 & 5

Form
4
Chapter 1 Functions Additional Mathematics

1.1 Functions 7. If the line intersects the graph at only one CHAP
point, then the graph is a function.
Explaining function by using graphical y 1
representation and notation Vertical line test
f
1. Function is a special relation where for every
object in domain, there is one and only image
in codomain. x
0
2. For example, every element in set X has only
one image in set Y.
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8. If the line intersects the graph at more than
a • • e one points, then the graph is not a function.
b • • f y
c • • g Vertical line test
d • • h
f
Set X Set Y
3. A function f, which maps x to (mx + n) can be 0 x
written as

f : x → mx + n or f(x) = mx + n
9. An absolute value function is a function
where x is the object and f(x) or (mx + n) is the that contains an algebraic expression within
image if x is under the function f. absolute value symbols.
4. Function is a relation of one-to-one or a relation 10. The absolute value function of x is written as
of many-to-one. f(x) = |x| and is defined by
(a) One-to-one relation
x if x  0
f(x) f(x) =  0 if x = 0
–x if x  0
f
f
y x • • y
2 1 1 11. The graph of a linear absolute value function
y
1 x • • y has a V-shaped.
2 2
y
x
0 x x
1 2
(b) Many-to-one relation f(x) = |x|

f(x) x
y = f(x) 0
f
x • 12. The discrete function is a function where the
y 1 • y points on the graph is real, separated and not
x •
2
connected by a straight line or curve.
f(x)
x
x 0 x
1 2
5. If given a graph of a relation, we can determine
whether the graph is a function or not by using
a vertical line test.
6. The vertical line test can be tested by drawing a x
line vertically on the graph. 0

1.1.1 3