The purpose of the graph is to present numerical facts in visual form so that students can understand quickly, easily and clearly. Thus, graphs are visual representations of collected data. Data can also be presented in the form of a table but a graphical presentation is simple and easier to understand. When there is a trend or comparison to be shown, then this approach is very effective.
In addition to the presentation of data, we can represent functions using graphs while solving them. Graphs show many input-output pairs in a small space, the visual information they provide usually makes relationships easier to understand. We generally construct graphs with the input values along the horizontal axis and the output values along the vertical axis. For each input value, a function has only one output value.
Consider linear functions (which means the highest degree of the variable is one), the graphs of these type of functions are straight lines. In order to determine whether a graph represents a function we can use the vertical line test. If the graph has a downward slant, it indicates a negative slope. This is exactly predicted from the negative constant rate of change in the equation for the function.
A geometric figure designed by two rays sharing a common endpoint (also called the vertex) is known as an angle. The two rays are called the sides of the angle, the size of an angle often measured using degree and radian (also abbreviated as rad). These angles are categorized into various types based on the value of their measures. They are:
- Acute angle: If the measure of the angle is less than 90 degrees, then it is an acute angle.
- Right angle: If the measure of the angle is equal to 90 degrees, then it is called a right angle.
- Obtuse angle: If the measure of the angle is greater than 90 degrees but less than 180 degrees, then it is an obtuse angle.
- Straight angle: If the measure of the angle is equal to 180 degrees, then it is a straight angle.
- Reflex angle: If the measure of the angle is greater than 180 degrees but less than 360 degrees, then it is a reflex angle.
- Complete or full angle: If the measure of the angle is equal to 360 degrees, then it is a complete or full angle.
Apart from the measurements of individual angles, they are special relationships between them, which can be formed by adding them. Suppose, when two angles add up to 90 degrees then they are called complementary angles and if two angles add up to 180 degrees, then they are called supplementary angles. That means complementary angles form a right angle and supplementary angles form a straight line.