Title: Jul 7 8:49 PM (1 of 18)

Transcription

1 Title: Jul 7 8:49 PM (1 of 18)

2 Let's review some of the terms used to describe functions. domain: continuous: bounded: even: the set of values from which the input values, x values, are taken every point in the domain of the function has a value the function's graph lies entirely between two horizontal lines (A graph can be bounded above or below or completely bounded.) the function's graph is symmetric about the y axis odd: the function's graph is symmetric about the origin increasing: decreasing: the function's graph is headed upward as it moves from left to right the function's graph is headed downward as it moves from left to right For more definitions, go to the precalculus link and click on "definitions". Title: Jul 8 10:48 AM (2 of 18)

3 The Identity Function degree one domain all real numbers range all real numbers continuous throughout its domain unbounded odd increasing end behavior rises to the right, falls to the left Title: Jul 7 9:39 PM (3 of 18)

4 The Squaring Function degree two domain all real numbers range all real numbers greater than or equal to zero continuous throughout its domain bounded below by the x axis even decreasing on, increasing on end behavior rises to the right and rises to the left Title: Jul 8 11:31 AM (4 of 18)

5 The Cubing Function degree three domain all real numbers range all real numbers continuous throughout its domain unbounded odd increasing end behavior rises to the right, falls to the left Title: Jul 8 11:44 AM (5 of 18)

6 The Reciprocal Function domain all real numbers except zero range all real numbers except zero continuous throughout its domain unbounded odd decreasing Title: Jul 8 11:57 AM (6 of 18)

7 The Square Root Function domain all real numbers greater than or equal to zero range all real numbers greater than or equal to zero continuous throughout its domain bounded below by the x axis increasing on its domain Title: Jul 8 12:16 PM (7 of 18)

8 The Exponential Function domain all real numbers range all real number greater than or equal to zero continuous bounded below by the x axis increasing Title: Jul 8 12:24 PM (8 of 18)

9 1 1 The Natural Logarithm Function domain range continuous increasing all real numbers greater than zero all real numbers Title: Jul 8 1:05 PM (9 of 18)

10 The Sine Function domain all real numbers range [ 1, 1] continuous bounded above and below by the line y=1 and y= 1 periodic Title: Jul 8 1:15 PM (10 of 18)

11 The Cosine Function domain all real numbers range [ 1, 1] continuous bounded above and below by the lines y=1 and y= 1 even periodic Title: Jul 8 1:17 PM (11 of 18)

12 The Absolute Value Function domain all real numbers range all real number greater than or equal to zero continuous bounded below by the x axis even decreasing for negative x's and increasing for positive x's rises to the right and left Title: Jul 8 1:18 PM (12 of 18)

13 The Greatest Integer Function floor ceiling (sometimes called the least integer function domain range discontinuous all real numbers the positive and negative integers Title: Jul 8 1:20 PM (13 of 18)

14 The Logistic Function domain all real numbers range (0, 1) continuous bounded above and below by the lines y=0 and y=1 increasing Title: Jul 8 1:46 PM (14 of 18)

15 Here are two functions, one red, and the other blue. What can you say about the end behavior of these two functions? One of the functions is is. The other Which function is which? Title: Jul 8 2:45 PM (15 of 18)

16 Here are the graphs of and on [0,1]. Which one is which? Title: Jul 8 2:53 PM (16 of 18)

17 Here are the graphs of Which is which? and Title: Jul 8 3:10 PM (17 of 18)

18 Which of the basic functions have asymptotes? Vertical Horizontal Assignment: textbook (lesson 1.3) 1 28 Title: Jul 8 3:24 PM (18 of 18)