# Graphing Techniques and Types of Graph

For secondary schools, calculators are used for the GCE N(T), N(A), O and A-Level Examinations. The main brands that are allowed include, CASIO, CANNON and Sharp. (Refer to the full list of approved models here).

At the JC-Level, graphing calculators can be your best tool to solve equations and plot sketches for graphs. As of 2023, graphing calculators are allowed for use ONLY in subjects examined at H1, H2 and H3 Levels of the GCE A-Level Curriculum. The main brands that are allowed include CASIO and Texas instruments. (Refer to the full list of approved models here)

While calculators and graphing calculators can be effective in solving mathematics questions, do note that the approved periods for some of the calculators end on 2024, and students should check with a teacher or our tutors if they remain acceptable.

## Graphing Techniques

A sketch of a graph refers to an outline or a rough drawing of the graph. To be able to sketch, you need to recognize the equation of the graphs and its accompanying shape, this can be achieved by identifying 3 main factors.

1. Shape and Symmetry
2. X and Y intercepts and intersection
3. Asymptotes

By identifying the qualities, you will be able to label the axes and turning points. The following section explains the the types of graph as shown above.

For graphs that are a straight line, the graph follows the equation y = mx + c where m is the gradient/slope and c is the y-intercept. This is shown in the top right and middle left diagrams.

To sketch a straight line graph on the graphing calculator:

Enter stats mode/ look for the function where the calculator indicates “y=mx+c”.

• Insert the numbers accordingly.
• Press zoom, 6 to select the “Zstandard” and the graph is displayed in the standard window setting

To calculate the X intercept on the graphing calculator:

• Press 2nd, trace, 2. The interface should indicate “2:zero”
• Use the arrow keys to move the cursor to the left of the root and press enter. This will display the x-intercept.

To calculate the Y intercept on the graphing calculator:

• Press 2nd, trace, 1. The interface should indicate “1:value”
• Press 0, enter to get the y-intercept

An asymptote is a line whereby the curve approaches the axis but doesn’t touch and goes towards infinity. In the top left corner, the graph demonstrates an asymptote.

Axes of symmetry refer to vertical and horizontal lines of symmetry where the two sides of a graph look like mirror images of each other. This should look similar to the middle right diagram.

To sketch a quadratic, “c” shaped, or a graph that has an axes of symmetry on the graphing calculator:

• Press Y=  and key in the equation of the graph accordingly.
• Adjust the window settings by pressing the window, next, indicate the boundaries of the display for example xmin = -5, xmax = 5, xscl= -1, ymin= -1, ymax= 10, yscl = 1, Xres= 1.
• Press graph and the graph is displayed in the window based on the window settings set above.

To get y-intercept:

• Press 2nd, trace, 1. The interface should indicate “1:value”
• Press 0, enter to get the y-intecept.

To get the minimum point (assuming its a smiley face shaped)

• Press 2nd, trace, 3. The interface should indicate “3:minimum”
• Move the cursor on the screen towards the left or close to the minimum point and press enter
• Move the cursor to the right of the root and press enter.
• Press enter again to obtain the minimum point.