Section 2.3 – Functions and their graphs – (will fill in during class lecture)

What does a graph represent?

a) the graph represents ALL the ordered pairs that are on the function b) we graph by plotting points (x,y) by picking values for x c) how many points do we need depends on what we know about the basic shape of the graph

  What are intercepts?

a) the x intercept crosses the x axis and that happens only when y = 0 ; point (x,0) b) zero is another word for x intercept only ; zeros are -2 and 3 c) the y intercept crosses the y axis and that happens only when x = 0 ; point (0,y)

  Example  :  Use  the  graph  below  to  determine  the  following:  the  domain  of  the  function,  range  of  the  function,  x  intercept,  y  intercept.  

 

Domain in interval notation:

Domain in interval notation:

Range in interval notation:

Range in interval notation:

x – intercept:

x – intercept:

y – intercept:

y – intercept:

zeros:

zeros:

Example, Create a table of values to graph the following function and identify the type of the function. State the the domain and range in interval notation.

 

f x = −x 2 −1

()

 

 

 

 

 

 

 

g x = x 3 +1

()

   

 

 

 

 

 

()

h x = x + 2  

Domain in interval notation:

Domain in interval notation:

Domain in interval notation:

Range in interval notation:

Range in interval notation:

Range in interval notation:

Example,  Graph  the  following  linear  functions.  State  the  domain  and  the  range  in  interval  notation. !

!

𝑓 𝑥 = 4𝑥 − 3

𝑔 𝑥 =− 𝑥+2

Domain in interval notation:

Domain in interval notation:

Domain in interval notation:

Range in interval notation:

Range in interval notation:

Range in interval notation:

 

!

𝑔 𝑥 = 𝑥 !