2.1 day 1: Step Functions “Miraculous Staircase” Loretto Chapel, Santa Fe, NM Two 360 o turns without support!

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2.1 day 1: Step Functions “Miraculous Staircase” Loretto Chapel, Santa Fe, NM Two 360 o turns without support!

Limit notation: “The limit of f of x as x approaches c is L.” So:

The limit of a function refers to the value that the function approaches, not the actual value (if any). not 1

Properties of Limits: Limits can be added, subtracted, multiplied, multiplied by a constant, divided, and raised to a power. (See page 58 for details.) For a limit to exist, the function must approach the same value from both sides. One-sided limits approach from either the left or right side only.

At x=1:left hand limit right hand limit value of the function does not exist because the left and right hand limits do not match!

At x=2:left hand limit right hand limit value of the function because the left and right hand limits match

At x=3:left hand limit right hand limit value of the function because the left and right hand limits match

“Step functions” are sometimes used to describe real-life situations. Our book refers to one such function: This is the Greatest Integer Function. The TI-83 contains the command, but it is important that you understand the function rather than just entering it in your calculator.

Greatest Integer Function:

The greatest integer function is also called the floor function. The notation for the floor function is: Some books use or.

The calculator “connects the dots” which covers up the discontinuities. The TI-83 command for the floor function is int (x). Graph the floor function for and. Y= CATALOG I int( int (x)

Go toY= Highlight the slant line to the left. ENTER GRAPH The open and closed circles do not show, but we can see the discontinuities. The TI-83 command for the floor function is int (x). Graph the floor function for and. Pressuntil the line appears dotted

Least Integer Function:

The least integer function is also called the ceiling function. The notation for the ceiling function is: Least Integer Function: The TI-89 command for the ceiling function is ceiling (x). Don’t worry, there are not wall functions, front door functions, fireplace functions!