Page 8 - Focus SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 1 Functions
(b) This is a graph of y as a function of x. The vertical 2. The function can be written as p : x → 4x
line intersects the graph at only one point. which is read as “function p maps x to 4x” or
p(x) = 4x which is read as “4x is the image of
y
In this graph, for object x under the function p”. Input value x is
any one input value known as the object while 4x is known as the
x, there is at most
x one output value y. image.
O
3. The letter f is frequently used to denote a
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function. f(x) represents the output of a function
(c) This is a graph of y as a function of x. The vertical f when the input is x.
line intersects the graph at only one point, except 4. Other letters can also be used to represent
for the line x = 1 which does not intersect at any certain quantities in a function, such as the
point in the graph. letter A for area and h for height. For example, Form 4
2
y h(t) = 9.8t – 3.6t can be used to represent the
In this graph, for height, h meters, reached by a ball t seconds after
any one input value
x, there is one being tossed.
x output value y.
0 5. When an equation involving two variables is
x = 1
used to represent a function, such as y = 2x + 3,
this equation can be written as f : x → 2x + 3 or
SPM Tips f(x) = 2x + 3.
Input Output Function
If there exists a vertical line which does not intersect
the graph at any value of x as in Example 2(c), then x f(x) f(x) = 2x + 3
the function is undefined for that value of x.
Generally, f(x) is the value of y for a function.
Hence, y = f(x).
Try Question 3 in ‘Try This! 1.1’

REMEMBER!
(b) Function notation
The notation f(4) represents the value of a function
1. Function notation is a method to represent when the input value is 4. 4 is not the output value.
functions. Likewise, f(4) does not mean f × 4.
For example,

• The perimeter, p, of a square 3
In with sides x units is four times
words x. (a) In the following diagram, set Y contains the

images of the objects in set X.

In • Perimeter, p = 4x.
formulae 4 2
9 3
16 4
In
function • p(x) = 4x. Set X Set Y
notation Write the relation between set X and set Y by

using function notation.
Hence, p(5) denotes the perimeter of a square
with sides 5 units. The notation p(5) represents (b) The volume, V, of a sphere with radius r units is
the output for the function when the input value 4 πr . Write the relation between the volume of the
3
is 5. 3
sphere and its radius by using function notation.

5