Objective: You will learn about what graphs can tell us. Twelve basic functions. And we will analyze functions graphically.

1
Chapter 1.3

• Objective You will learn about what graphs can
  tell us. Twelve basic functions. And we will
  analyze functions graphically.

2
Write down everything you know about the function
f(x) x² including its graph.
3
Twelve Basic Functions
4
Example

• Nine of the functions have a domain of all real
  numbers. Which three do not?
• Answer
• The Reciprocal Function
• The Square Root Function
• The Natural Log Function

5
Example

• Which function has a domain of all real numbers
  except 0? Why isnt 0 in the domain?
• Answer
• The reciprocal function because you can not
  divide by 0.

6
Example

• Which two functions have no negative numbers in
  their domains? Of these two, which one is defined
  at zero?
• Answer
• The square root and the natural log functions.
• Square Root is defined at 0.

7
Looking for continuity

• Only two of the twelve functions have points of
  discontinuity. Are these points in the domain of
  the function?
• Answer The reciprocal function and integer
  function are the only non continuous/broken
  graphs. The reciprocal function has infinite
  discontinuity at x 0 and 0 is not in the domain
  of the function. Since y 1/x is continuous for
  every point in its domain, it is called
  continuous.

8
Looking for boundedness

• Only three of the twelve basic functions are
  bounded (above and below).
• Which three?
• Answers Sine, Cosine, Logistic Functions

9
Looking for Symmetry

• Three of the twelve basic functions are even.
  Which are they?
• Answers y x², y cos(x), y x

10
Homework

• Pg. 113
• 1 12, 13 33 odd