​Learning Objectives

​After studying this topic, students are able to:

​• represent situations in words or as linear functions

​• plot graphs of linear functions

​• learn how to recognize lines parallel to the x-axis or y-axis

​• interpret graphs related to rates of change

​11.1 Functions

​A function shows the relationship between two variables.

You often use x and y to represent two variables, but you can use other letters.

​

​Example:

Maryam is 6 years older than his brother Jamal.

​ m = j + 6

​So, when Jamal is 12 years old, Maryam will be:

​ m = 12 + 6 = 18 years old

​11.2 Graph of functions

​Given a function y = x + 3.

When x = ​2, then y = 2 + 3 = 5

​When x = -4, then y = -4 + 3 = -1

​

​You can display values of x and the corresponding values of y in a table

​11.2 Graph of functions

​Given a function y = x + 3.

​

​

​

Q: Is the point (5,9) located on the line?

​

Check:

y = x + 3

when x=5, y=5+3=8,

So, the point (5,8) is on the line, but

the point (5,9) is NOT on the line. ​

​

​

​11.3 Lines parallel to the axes

​A and B are on a line parallel to

​the y-axis. The line is x = 4.

​

​​C and D are on a line parallel to

​the y-axis. The line is x = -2.

​​

A and D are on a line parallel to

​the x-axis. The line is y = 2.

​​

B and C are on a line parallel to

​the x-axis. The line is y = -3.

​

​11.4 Interpreting graphs

Graphs can show how the value of variable changes with time.

​

Example:​

​This graph shows the distance

travelled by a runner in a 5 km race.