1. Some Common Functions and their Graphs – Constant Functions & Linear Functions

2. What is a constant function?
Constant Functions
What is a constant function?
A function in the form y = c or f(x) = c, where c is a constant, is called a constant function.

3. Constant Functions What is a constant function?
For example, y = 1 and f(x) = –2 are constant functions.

4. Consider the constant function y = 1. x –2 2 y 12 y 1
◄ The value of y is always equal to 1, for any value of x. y x
(–2, ) 1
(0, ) 1
(2, ) 1
y = 1
y-coordinates of all the points on the line are equal to 1
A straight line parallel to the x-axis

5. Graph of y = c O y x
c 0 O y x
c= 0 O y x
c 0
(0, c)
(0, c)
(0, c)
The graph of a constant function is a horizontal line passing through (0, c).

6. Follow-up question
The figure shows the graph of a constant function. Write down the algebraic representation of the function. x y
2  2 4
∵ The graph is a horizontal line which cuts the y-axis at (0, –3).
(0, –3)
∴ The required function is y = –3.
y = f(x)

7. Linear Functions
A function in the form y = ax + b or f(x) = ax + b, where a and b are constants and a  0, is called a linear function of x.
Example:
(i) y = 3x – 1
linear functions of x
(ii) f(x) = –2x + 5

8. The graph cuts the x-axis at P.
Graph of y = ax + b O y x
y = ax + b
The graph cuts the x-axis at P. P

9. The graph cuts the y-axis at Q.
Graph of y = ax + b O y x
y = ax + b Q
The graph cuts the y-axis at Q.
x-intercept a b -

10. Graph of y = ax + b x-intercept y-intercept
The graph of a linear function is a straight line. It has only one x-intercept and one y-intercept.

11. Graph of y = ax + b a 0 a 0 O y x O y x
The value of y increases as x increases.
The value of y decreases as x increases.

12. Follow-up question
The figure shows the graph of the linear function y = f(x). Write down the x-intercept and the y-intercept of the graph. x y
2  4 2 2 4
∵ The graph cuts the x-axis and the y-axis at (2, 0) and (0, 3) respectively.
y = f(x)
(0, 3)
(2, 0)
∴ x-intercept = 2 and
y-intercept = 3