Page 14 - Pra U STPM 2022 Penggal 1 - Mathematics (T)

Mathematics Term 1 STPM Chapter 1 Functions
Graphs of linear, quadratic and cubic-functions

The simplest algebraic function is the linear function, usually in the form f(x) = ax + b, where a and b are
rational numbers, either positive or negative. The graph of a linear function is a straight line, and a is known 1
as the gradient and b the intercept on the y-axis. The graph of y = ax + b for different values of a and b are
as follows:
Linear function
f(x) = ax + b
y y y y

x x x x
O O O O

a . 0, b . 0 a . 0, b , 0 a , 0, b . 0 a , 0, b , 0

Figure 1.9
The shape of the graphs for a quadratic and a cubic function are as shown below.
Quadratic function Cubic function
2
3
2
f(x) = ax + bx + c f(x) = ax + bx + cx + d
or or

a . 0 a , 0 a . 0 a , 0

Figure 1.10
Notice that the graph of a quadratic function has one stationary point, whereas a cubic function has two
stationary points.

Example 6

Sketch the graphs of the following functions.
2
(a) f(x) = x + 4x + 5, (b) f(x) = –2x + 3x + 1.
2
Solution: (a) f(x) = x + 4x + 5 can be expressed as
2
f(x) = (x + 2) – 4 + 5, by completing the square
2
= (x + 2) + 1
2
The graph cuts the y-axis when x = 0, i.e. y = 5.
As x → `, y → `
Similarly when x → –`, y → `.
When x = –2, y = 1 is the minimum value of f(x).
2
Hence the graph of y = x + 4x + 5 is as shown below.
y
2
y = x + 4x + 5
5

1
x
–2 0

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01a STPM Math T T1.indd 11 3/28/18 4:20 PM