Graphing Functions
How do I graph the function y = f(x)?
- A point lies on the graph of if
- The horizontal axis is used for the domain
- these are the x-values
- The vertical axis is used for the range
- these are the corresponding y-values
- Graphing a function can involve any or all of the following skills
- creating a table of values
- knowing the general shapes and characteristics of different types of graphs
- finding axis intercepts
- finding turning points (including maxima and minima)
- identifying asymptotes
What is the difference between “draw” and “sketch”?
- 'Sketch' questions will not provide a detailed grid to draw the graph on
- A sketch is meant to show key features of a graph
- It does not need to be perfectly to scale
- It does not need to plot points precisely
- When asked to sketch you should:
- Show the correct general shape
- Label any key points such as the intersections with the axes
- Label the axes
- Label the graph by giving its function or equation
- A sketch is meant to show key features of a graph
- 'Draw' questions will always provide a detailed grid to draw the graph on
- A drawing of a graph is meant to be as accurate as possible
- When asked to draw you should:
- Use a ruler for any straight lines
- Draw to scale
- Plot any points precisely
- Join points with a straight line or smooth curve
- Label any key points such as the intersections with the axes
- Label the axes
- Label the graph by giving its function or equation
Can my calculator help me sketch/draw a graph?
- Your calculator may be able to display graphs of functions
- If so make sure you are familiar with how this feature works
- This can be useful for checking your work
- It can also help with identifying
- the general shape of a graph
- axis intercepts
- turning points (including maxima and minima)
- But be careful, especially on 'show that' questions
- Make sure key parts of an answer are backed up by working
- Marks may depend on this