The document discusses drawing graphs of different types of functions, including linear, quadratic, cubic, and reciprocal functions. It provides the general forms of each type of function, describes the steps to draw their graphs which include constructing a table of values, plotting points, and joining the points. As an example, it shows the graph of a reciprocal function f(x) = 1/x for -1 ≤ x ≤ 1.5, which forms a hyperbola shape.

1. GRAPHS OF FUNCTIONS II MATHEMATICS Form 5 Chapter 2

3. General form:

4. General form:

5. General form:

6. 2.1 Understand and use the concept of graphs functions At the end of the lesson, students should be able to: Draw the graph of a) a linear function, where a and b are constant b) a quadratic function, where a , b and c are constant c) a cubic function, where a , b and c are constant d) a reciprocal function, where a is constant and

7. Steps to draw a graph: Construct a table of values for a chosen range of x values. Draw the x-axis and the y-axis and use a suitable scale for each axis starting from the origin. Plot the x and y values as coordinate pairs on the Cartesian plane. Join the points to form a straight line (using ruler) or a smooth curve (without using ruler). Label the graph.

8. RECIPROCAL GRAPH General form: where a is a constant,

9. Example: Draw a graph for the function for . ANSWER

10. Scale: 1 cm : 1 unit at x-axis 2 cm : 2 units at y-axis 1.5 2 3 6 12 -12 -6 -3 -2 -1.5 y 4 3 2 1 0.5 -0.5 -1 -2 -3 -4 x

11. Characteristics of reciprocal graphs: Reciprocal graphs consist of TWO different parts. The shape of the graphs are known as HYPERBOLA.

12. WORKSHEET

13. Summary or or or or 1 2 3 -1 Reciprocal Cubic Quadratic Linear Shape of the function Highest power of variable x General form Types of function