×

### Let's log you in.

or

Don't have a StudySoup account? Create one here!

×

or

21

0

13

# Class Note for MATH 1314 with Professor Flagg at UH

Marketplace > University of Houston > Class Note for MATH 1314 with Professor Flagg at UH

No professor available

These notes were just uploaded, and will be ready to view shortly.

Either way, we'll remind you when they're ready :)

Get a free preview of these Notes, just enter your email below.

×
Unlock Preview

COURSE
PROF.
No professor available
TYPE
Class Notes
PAGES
13
WORDS
KARMA
25 ?

## Popular in Department

This 13 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 21 views.

×

## Reviews for Class Note for MATH 1314 with Professor Flagg at UH

×

×

### What is Karma?

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 02/06/15
Math 1314 Lesson 12 Curve Sketching One of our objectives in this part of the course is to be able to graph functions In this lesson we ll add to some tools we already have to be able to sketch an accurate graph of each function From prerequisite material we can nd the domain y intercept and end behavior of the graph of a function and from the last two sections we can learn much about a function by analyzing the rst and second derivatives We also know how to find the zeros of some functions We ll expand that group of function before we continue to curve sketching The Rational Zeros of a Polynomial Function The rational zeros of a function are the zeros of the function that can be written as a fraction such l as 2 or Somet1mes we can nd the ratlonal zeros of a functlon by factor1ng Example 1 Find the rational zeros f x x3 16x Example 2 Find the rational zeros fx x4 1 1x2 18 Math 1314 Lesson 12 Page 1 of 13 Note that zeros that are square roots are NOT rational roots Imaginary solutions to the equation f x 0 such as i 3139 are NOT rational roots Sometimes we won t be able to factor the function Then we ll need another method We ll use a theorem called the Rational Zeros Theorem First we ll nd all of the possible rational zeros of a given function using the Rational Zeros Theorem Then we can use a calculator or synthetic diVision to determine which 7 if any 7 of the possible rational zeros are actually zeros of the function Here s the theorem Rational Zeros Theorem Suppose fx anxquot anilxx391 a0 where an at 0 and do at 0 and all ofthe coefficients of the polynomial are integers If x E is a rational zero of the function where p and q have no common factors then p is a q factor of the constant term a0 and q is a factor of the leading coefficient an Example 3 Find the possible rational zeros of fx 2x3 3x2 8x 4 Example 4 Find all rational zeros of f x x3 6x2 3x 10 or state that there are none Math 1314 Lesson 12 Page 2 of 13 Example 5 Find all rational zeros of f x x3 7x2 16x 12 or state that there are none Example 6 Find all rational zeros of fx x4 4x3 3x2 4x 4or state that there are none Math 1314 Lesson 12 Page 3 of 13 Example 7 Find all rational zeros of f x x3 3x2 1 or state that there are none Example 8 Find all rational zeros of f x x4 5x3 4x2 or state that there are none Math 1314 Lesson 12 Page 4 of 13 Example 9 Find all rational zeros of f x x3 4x2 4x 16 or state that there are none Curve Sketching Now we ll turn our attention to graphing functions You will need to be able to use the following guide to sketch the graphs of functions A Guide to Curve Sketching 1 Determine the domain off 2 Find the rational x intercepts and y intercept of the function If there are no rational x intercepts say so Determine the end behavior of the function For an exponential function determine any horizontal asymptotes Determine where the function is increasing and where it is decreasing Find the x and y coordinates of any relative extrema Determine where the function is concave upward and where it is concave downward Find the x and y coordinates of any points of in ection If necessary plot a few additional points to determine the shape of the graph 0 Sketch the function was wew Math 1314 Lesson 12 Page 5 of 13 Recall the generalizations about end behavior of a polynomial function from College Algebra Example 10 Use the guide to curve sketching to sketch f x x4 4x3 Math 1314 Lesson 12 Page 6 of 13 Sometimes a function has some zeros that are not rational We may occasionally give you the approximate zeros of the function and ask you to complete the rest of the guide to curve sketching Example 11 Use the guide to curve sketching to sketch fx x3 6x2 15x3 Note the approximate zeros of the function are 022 172 and 7 94 Math 1314 Lesson 12 Page 7 of 13 Example 12 Use the guide to curve sketching to sketch fx x3 7x2 16x 12 Note we found the rational zeros in example 5 Math 1314 Lesson 12 Page 8 of 13 Example 13 Use the guide to curve sketching to sketch fx x3 8x2 19x 12 Math 1314 Lesson 12 Page 9 of 13 Example 14 Use the guide to curve sketching to sketch f x xe Math 1314 Lesson 12 Page 10 of 13 For the next two problems you are given all of the information listed in the guide to curve sketching You just need to use it to graph the function Example 15 Sketch the function if you are given the following information X intercept 0 0 4 0 y intercept 0 0 end behavior T T relative minimum 3 27 increasing intervals 3 co decreasing intervals 000 03 points of in ections 0 0 2 16 concave upward intervals 00 0 and 200 concave downward intervals 0 2 Math 1314 Lesson 12 Page 11 of 13 Example 16 Sketch the function if you are given the following information X intercepts 0 0 1 0 and 2 0 y intercept 0 0 end behavior T T relative maximum 061 020 relative minimum 164 062 and 0 0 increasing intervals 164 061 and 0 00 decreasing intervals oo 164 and 061 0 points of in ections 027 009 and 123 027 concave upward intervals 00 123 and 027 00 concave downward intervals 123 027 Math 1314 Lesson 12 Page 12 of 13 Example 17 Here is the graph of a polynomial function Which of the statements below isare true The function has three zeros The graph of the function is increasing on one interval and decreasing on two intervals The graph of the function has one relative maximum and one relative minimum The graph of the function has two in ection points The function could be a quartic function 4 11 degree with a positive leading coefficient V eP Nf From this section you should be able to Find any rational zeros of a 3ml or 4th degree polynomial Use the guide to curve sketching to sketch the graph of a polynomial or exponential Sketch a graph of a function given all of the information from the guide to curve sketching Answer questions about the graph of a function given the graph of the function Math 1314 Lesson 12 Page 13 of 13

×

×

### BOOM! Enjoy Your Free Notes!

×

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

Steve Martinelli UC Los Angeles

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Janice Dongeun University of Washington

#### "I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

Steve Martinelli UC Los Angeles

Forbes

#### "Their 'Elite Notetakers' are making over \$1,200/month in sales by creating high quality content that helps their classmates in a time of need."

Become an Elite Notetaker and start selling your notes online!
×

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com