Your SlideShare is downloading. ×
0
PP1 Presentation
PP1 Presentation
PP1 Presentation
PP1 Presentation
PP1 Presentation
PP1 Presentation
PP1 Presentation
PP1 Presentation
PP1 Presentation
PP1 Presentation
PP1 Presentation
PP1 Presentation
PP1 Presentation
PP1 Presentation
PP1 Presentation
PP1 Presentation
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

PP1 Presentation

357

Published on

Published in: Education
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
357
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
4
Comments
0
Likes
0
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. Chapter 1<br />Section 1.1<br />Functions and their Representation<br />
  • 2. Domain and Range<br />Domain<br />The set A or X values of an equation of function<br />Range<br />The set of B or Y values of an equation<br />Also known as output values<br />These numbers include:<br />Individual numbers<br />All real numbers<br />Can include +/- Infinity<br />Can also exclude zero<br />
  • 3. Functions and their Representation<br />This graph passes the vertical line test.<br />Functions<br />Each element (input) matches and is set to exactly one and only one output. (A to B)<br />Testing a function<br />Vertical line test<br />Method used for determining if a graph is or is not a function<br />Wikipedia. 2010.<br />Functions. <br />
  • 4. Vertical Line Test<br />What exactly does it do?<br />Tests that there is only one Y output for an X input.<br />Is a function<br />Not a function<br />UNCW EDU<br />T. Barron & S. Kastberg.<br />University of Georgia<br />
  • 5. Inverse Functions<br />Exception to the vertical line test?<br />Inverse Functions<br />Function are A to B (X,Y)<br />Inverse functions are B to A (Y,X)<br />Ex. To left is function along with it’s inverse.<br />Think Quest. 2010.<br />Inverse Functions.<br />
  • 6. Inverse Functions<br />Horizontal Line Test<br />Used in cases of inverse functions<br />Determines if the graph is a function or not<br />Below is example of a plot and its inverse<br />
  • 7. Representations of Functions<br />Four possible ways to represent a function<br />Verbally<br />Description in words<br />Visually<br />By a graph<br />Numerically<br />Table of values<br />Algebraically<br />Explicit formula<br />
  • 8. Increasing Functions<br />The Y-value increases as the X-value increases<br />f(x1) < f(x2) whenever; x1 < x2<br />Increasing sections of a graph<br />Math Is Fun. 2010.<br />Increasing Functions<br />
  • 9. Decreasing Functions<br />The Y-value decreases as the X-value increases<br />f(x1) > f(x2) whenever; x1 < x2<br />Decreasing section of a graph<br />Math Is Fun. 2010.<br />Decreasing Functions<br />
  • 10. Chapter 1<br />Section 1.2<br />Catalog of Essential Functions<br />
  • 11. Mathematical Modeling<br />What is mathematical modeling?<br />Mathematical representation (often by means of a function or an equation) of real-world phenomenon<br />Types of Models<br />Linear<br />y=f(x)=mx+b<br />Polynomials<br />P(x)= x2 − 4x + 7<br />Cubic Functions<br />C(x)=ax3 + bx2 + cx + d<br />
  • 12. Linear Equations<br />Graph of the function is a line<br />y=mx+b<br />y is the range<br />m is the slope<br />b is the y-intercept<br />Wikipedia.org. 2010.<br />Linear Functions.<br />
  • 13. Polynomial Functions<br />Graph of the function depends on the degree<br />Degree<br />The power of the coefficient and its variable<br />P(x)= x2 − 4x + 7<br />Degree of the above equation is 2.<br />Example to left is polynomial of degree 2<br />Wikipedia.org. 2010.<br />Polynomial Functions<br />
  • 14. Cubic Functions<br />A polynomial of a degree 3<br />C(x)=ax3 + bx2 + cx + d<br />Wikipedia.org. 2010.<br />Cubic Functions.<br />
  • 15. Other Type of Functions<br />Rational Functions<br />Wikipedia.org. 2010.<br />Trigonometric Functions<br />f(x)=sin x<br />f(x)=cos x<br />f(x)=tan x<br />To right is example of f(x)=sin x<br />Analyze Math. 2007.<br />Sin x Function<br />
  • 16. Other References<br />Wikipedia. http://www.wikipedia.org/<br />Google Images. http://www.google.com/<br />Essential Calculus: Early Transcendentals. James Stewart. pp(1-18). 2007.<br />

×