HSC Higher Mathematics 1st Paper Note 8th Chapter Functions and graph of functions
HSC Higher Mathematics 1st Paper Note 8th Chapter Functions and graph of functions. The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x). So, the graph of a function if a special case of the graph of an equation. Example 1. Let f(x) = x2 – 3. Recall that when we introduced graphs of equations we noted that if we can solve the equation for y, then it is easy to find points that are on the graph. We simply choose a number for x, then compute the corresponding value of y. Graphs of functions are graphs of equations that have been solved for y! The graph of f(x) in this example is the graph of y = x2 – 3. It is easy to generate points on the graph. Choose a value for the first coordinate, then evaluate fat that number to find the second coordinate. The following table shows several values for x and the function f evaluated at those numbers.
HSC Higher Mathematics 1st Paper Note 8th Chapter Functions and graph of functions
In the real world, it’s very common that one quantity depends on another quantity. For example, if you work in a fast food outlet, your pay packet depends on the number of hours you work. Or, the amount of concrete you need to order when constructing a building will depend on the height of the building. Open image in a new page The Cartesian plane This chapter is about functions (this is how we express relationships between quantities) and their graphs. The graph of a function is really useful if we are trying to model a real-world problem. (“Modeling” is the process of finding the relationships between quantities.) Sometimes we may not know an expression for a function but we do know some values (maybe from an experiment). The graph can give us a good idea of what function may be applied to the situation to solve the problem.
The purpose of this reference section is to show you graphs of various types of functions in order that you can become familiar with the types. You will discover that each type has its own distinctive graph. By showing several graphs on one plot you will be able to see their common features. Examples of the following types of functions are shown in this gallery: linear, quadratic, power, polynomial, rational, exponential, logarithmic, sinusoidal.
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