2. We’ve already graphed equations. We can graph functions in the same way. The thing to remember is that on the graph the f(x) or function value is the same as the y value. If we want to graph the function f (x) = 3x – 1, it is the same thing as graphing y = 3x – 1. We recognise this as a line with a slope 3 and y-intercept of -1

3. So to graph any functions given, simply write a y where you see f(x) and then graph with the same method as you did graphs of equations plugging in values for x and finding the corresponding y values and plotting the points. Also recall that domain is the x-values you can “legally” plug in and range is the y-values you get out. The other thing you need to know is how to tell from a graph if the graph is of a function or not. I’ll address this on the next screen

4. Recall that for a relation to be a function, for each x there can only be one y value. Let’s look at a couple of graphs. Look at different x values and see there is only one y value on the graph for it. x = 0x = 1 x = -1 x = -2 This IS a function x = 0x = 1 At x = 1 there are two y values. This then is NOT a function

5. From what we've just seen, we can tell by looking at a graph of an equation if it is a function or not by what we call the vertical line test. If a vertical line intersects the graph of an equation more than one time, the equation graphed is NOT a function. This is a function This is NOT a function This is a function

6. Acknowledgement I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint. www.slcc.edu Shawna has kindly given permission for this resource to be downloaded from www.mathxtc.com and for it to be modified to suit the Western Australian Mathematics Curriculum.www.mathxtc.com Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar www.ststephens.wa.edu.au