Graphing Functions (DP IB Analysis & Approaches (AA)): Revision Note

Graphing Functions

How do I graph the function y = f(x)?

• A point lies on the graph if 

• The horizontal axis is used for the domain

• The vertical axis is used for the range

• You will be able to graph some functions by hand

• For some functions you will need to use your GDC

• You might be asked to graph the sum or difference of two functions

  • Use your GDC to graph or 

  • Just type the functions into the graphing mode

What is the difference between “draw” and “sketch”?

• If asked to sketch you should:

  • Show the general shape

  • Label any key points such as the intersections with the axes

  • Label the axes

• If asked to draw you should:

  • Use a pencil and ruler

  • Draw to scale

  • Plot any points accurately

  • Join points with a straight line or smooth curve

  • Label any key points such as the intersections with the axes

  • Label the axes

How can my GDC help me sketch/draw a graph?

• You use your GDC to plot the graph

  • Check the scales on the graph to make sure you see the full shape

• Use your GDC to find any key points

• Use your GDC to check specific points to help you plot the graph

Key Features of Graphs

What are the key features of graphs?

• You should be familiar with the following key features and know how to use your GDC to find them

• Local minimums/maximums

  • These are points where the graph has a minimum/maximum for a small region

  • They are also called turning points

    • This is where the graph changes its direction between upwards and downwards directions

  • A graph can have multiple local minimums/maximums

  • A local minimum/maximum is not necessarily the minimum/maximum of the whole graph

    • This would be called the global minimum/maximum

  • For quadratic graphs the minimum/maximum is called the vertex

• Intercepts

  • y­­ – intercepts are where the graph crosses the y-axis

    • At these points x = 0

  • x – intercepts are where the graph crosses the x-axis

    • At these points y = 0

    • These points are also called the zeros of the function or roots of the equation

• Symmetry

  • Some graphs have lines of symmetry

    • A quadratic will have a vertical line of symmetry

• Asymptotes

  • These are lines which the graph will get closer to but not cross

  • These can be horizontal or vertical

    • Exponential graphs have horizontal asymptotes

    • Graphs of variables which vary inversely can have vertical and horizontal asymptotes

Intersecting Graphs

How do I find where two graphs intersect?

• Plot both graphs on your GDC

• Use the intersect function to find the intersections

• Check if there is more than one point of intersection

How can I use graphs to solve equations?

• One method to solve equations is to use graphs

• To solve 

  • Plot the two graphs  and  on your GDC

  • Find the points of intersections

  • The x-coordinates are the solutions of the equation

• To solve 

  • Plot the two graphs  and  on your GDC

  • Find the points of intersections

  • The x-coordinates are the solutions of the equation

• Using graphs makes it easier to see how many solutions an equation will have