Chapter 1 lesson E: Sign Diagrams

Sometimes we need to know when the function is positive, negative, zero or undefined without the whole picture = sign diagra

Sign Diagrams consist of :

• horizontal line (the x- axis)
• positive/negative signs indicating that the graph is above and below the x-axis.
• critical values: the numbers written below the line which are the graph's x-intercepts and points where is it undefined.

Examples: Drawing a sign diagram

 

sign diagram:

• a sign change occurs about a critical point for single factors such as (x+2) and (x-1). This indicates cutting of the x-axis
• no sign change occurs about the critical value for squared factors such as (x-2)^2. This indicates touching of the x-axis.
• function is undefined at x=0
• in general, when a factor has an odd power there is a change of sign about the critical value.
• when a factor has an even power there is NO change in sign about the critical value.
• example: draw a sign diagram : (x+3)(x-1) 
• let x+3 = 0 which equals x=-3
• let x-1= 0 which equals x=1

*sorry for the inconvenience but the question marks above, in the equations, are actually x.