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Chapter Contents

• Functions and Graphs
• 1. Introduction to Functions
• 2a. Domain and Range of a Function
• 2b. Functions from Verbal Statements
• 3. Rectangular Coordinates
• 4. The Graph of a Function
• 5. Graphing Using a Computer Algebra System
• Plot your own graph
• 6. Graphs of Functions Defined by Tables of Data
• 7. Continuous and Discontinuous Functions
• 8. Split Functions
• 9. Even and Odd Functions

• Comments, Questions?

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3. Rectangular Coordinates

A good way of presenting a function is by graphical representation.

Graphs give us a visual picture of the function.

The rectangular co-ordinate system consists of:

Normally, the values of the independent variable (generally the x-values) are placed on the horizontal axis, while the values of the dependent variable (generally the y-values) are placed on the vertical axis.

The x-value, called the abscissa, is the perpendicular distance of P from the y-axis.

The y-value, called the ordinate, is the perpendicular distance of P from the x-axis.

The values of x and y together, written as (x, y) are called the co-ordinates of the point P.

Play with this LiveMath function plotter. Enjoy!

LIVEMath

Example 1

Locate the points A(2 , 1) and B(-4 , -3) on the rectangular co-ordinate system.

(You need to put a scale on the axes and then put dots for the required points A and B. This answer is left to the reader...)

 

Example 2

Three vertices of a rectangle are A(-3 , -2), B(4 , -2) and C(4,1). Where is the fourth vertex D?

Answer

 

Example 3

Where are all points (x , y) for which x < 0 and y < 0?

Answer

Exercises

Q1 Where are all the points whose abscissas equal their ordinates?

Answer

Q2 Where are all the points (x, y) for which x = 0 and y < 0?

Answer