New User Special Price Expires in

Let's log you in.

Sign in with Facebook


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


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

Math 1311

by: Corina Johnson

Math 1311 MATH 1311

Corina Johnson
View Full Document for 0 Karma

View Full Document


Unlock These Notes for FREE

Enter your email below and we will instantly email you these Notes for Elementary Mathematical Modeling

(Limited time offer)

Unlock Notes

Already have a StudySoup account? Login here

Unlock FREE Class Notes

Enter your email below to receive Elementary Mathematical Modeling notes

Everyone needs better class notes. Enter your email and we will send you notes for this class for free.

Unlock FREE notes

About this Document

Day 1 math 1311 Notes. Functions of a given formula, domain and range
Elementary Mathematical Modeling
Yifan Wang
Class Notes
Math, modeling, Domain and range




Popular in Elementary Mathematical Modeling

Popular in Mathematics (M)

This 8 page Class Notes was uploaded by Corina Johnson on Monday February 22, 2016. The Class Notes belongs to MATH 1311 at University of Houston taught by Yifan Wang in Spring 2016. Since its upload, it has received 27 views. For similar materials see Elementary Mathematical Modeling in Mathematics (M) at University of Houston.


Reviews for Math 1311


Report this Material


What is Karma?


Karma is the currency of StudySoup.

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

Date Created: 02/22/16
Math 1311 Section 1.1 Functions Given by Formulas Topics:  Using function notation  Domain  Answering questions when given a formula functions  Using TI to compute function values and using the “Ans” feature of the calculator What is a function? Definition: A function is a rule that assigns to each element of one set (which we call the domain) exactly one element of some other set (which we call the range). Example 1: a. If you are driving across the country, you can write a function that gives the distance you have traveled. If you travel at 65 miles per hour, this could be your function: ???????????????????????????????? = ???????????????? ???????? ???????????????????? × ???????????????? = 65 × ???????????????? b. If you work at a clothing store, you can write a function that gives the amount of money you earn in a week. If you make $8.50 per hour, this could be your function: ???????????? = ℎ???????????????????? ???????????????? × ???????????????????????? ???????? ℎ???????????????? ???????????????????????? = 8.50 × ???????????????????????? ???????? ℎ???????????????? ???????????????????????? c. If you buy some clothing, you’ll have to pay sales tax. You can write a function that gives the amount of sales tax. If sales tax is 8.25%, this could be your function: ???????????????????? ???????????? = ???????????????? ???????? ???????????????????? × ???????????? ???????????????? = ???????????????? ???????? ???????????????????? × 0.0825  Functions involve both independent and dependent variables. We can choose values for the independent variable, so long as they make sense in the function. The value of a dependent variable depends on the value chosen for the independent variable.  We assign letters for the independent and dependent variables. You can use any letter you like, subject to a couple of rules. 1. You must precisely define your variables (including units) 2. A letter can stand for only one quantity in your function. With this in mind, we can rewrite the function above using mathematical notation: a. ???? = 65???? b. P=8.50h c. T=(0.0825)c In = 65???? , the independent variable is ???? and the dependent variable is ????. Name the independent variable and the dependent variable in the other two functions. Example 2: Are the following correspondences functions? If not, explain why. a) (1,3) (2,5) (1,5) (3,6) b) (1,2) (3,4) (5,6) (7,8) c) (1,2) (2,2) (3,4) (5,6) Definition: The domain is the set of values that work in the function. In each of our three cases of Example 1, only positive numbers make sense. You can’t drive or work a negative number of hours and clothing can’t have a negative cost. We would write the domain as [0, ) for each. This notation is called interval notation. Here is a summary of interval notation: (−3,5) means all ???? such that −3 < ???? < 5 [−3,5] means all x such that −3 ≤ ???? ≤ 5 [−3,5) means all x such that −3 ≤ ???? < 5 [−3,∞) means all x such that ???? ≥ 3 (−∞,5) means all x such that ???? < 5 (−∞,∞) means all real numbers Some functions have specific restrictions on the domain: Example 3: 5 a. State the domain ???? ???? = ????−1 b. State the domain ???? ???? = ???? √ 4 We can evaluate a function at various values: Example 4: ???? −2????+3 Suppose ???? ???? = 4 . Compute ????(0), ????(4), and ????(−3) . This can be done in the TI calculator by pressing and entering the formula in Y 1 Then press to set up a table. Make sure Indpnt is set to ask and Depend set to Auto. TblStart and ∆Tbl do not matter here. Finally, press and then enter the desired input values. Now for some applications: Example 5: The time it takes David to travel from Houston to Denver is a function of the average speed travelled. The distance between the two cities is about 1200 miles. Suppose ???? is the average speed of David’s car in miles per hour. Let ???? = ????(????) be the time it takes to get to Denver (in hours at the speed of ???? miles per hour). The formula for the function is 1200 ???? ???? = ???? a. What does ????(60) represent? b. Write (using function notation) an expression that shows the time it takes to get to Denver if David travels at an average speed of 75 miles per hour. Example 6: Suppose your weekly pay is a function of the number of hours that you work per week. Let ℎ represent the number of hours you work. Suppose your hourly pay rate is $8.50. Then ???? = ????(ℎ) is your weekly pay (before taxes!) in dollars. The formula for the function is ????(ℎ) = 8.50ℎ a. What does ????(20) represent? b. Write (using function notation) an expression that shows you pay for the week if you worked 34 hours. Functions of Several Variables Sometimes formulas involve more than one variable. In that case, you’ll need to define each of the independent variables. This is called a function of several variables. Example 7: You may be familiar with the formula for perimeter of a rectangle: ???? = 2???? + 2????. This is a function of two variables, ???? and ????. We can write it using function notation: ????(????,????) = 2???? + 2???? The domain for this function is a set of ordered pairs, such as (10, 8). Then ????(10,8) represents the perimeter of a rectangle with length 10 units and width 8 units. Example 8: Suppose the amount of money, ????, (given in dollars) spent at Lowe’s for flooring is a function of the area of a room in square feet, ????. The cost, ????, of the flooring is given in dollars per square yard. Then ???? = ????(????,????) gives the cost of the flooring. The formula for this function is ???????? ???? ????,???? =) 9 a. What does M(1000,24) represent? b. Write using function notation an expression for the cost of flooring for a room with 750 square feet with hardwoods that cost $15.89 per square yard. Example 9: If you borrow ???? dollars at a monthly interest rate ???? (written as a decimal) and wish to pay off the loan in ???? months, your monthly payment can be expressed as the function ???? = ????(????,????,????) given in dollars. The formula for this is ???? ???? ????,????,???? =) ????????(1 + ????) (1 + ????) − 1 Find the monthly payment if you borrow $15,000 at 4% interest for 4 years. Using the “Ans” feature of the graphing calculator Sometimes, evaluating functions of several variables using your calculator becomes complicated. If this is the case, you can evaluate part of your problem and then use that answer as you continue computing. Locate the “Ans” button on your calculator. It’s the 2 ndof the key next to the enter button. To access the “Ans” feature, you’ll need to press 2 ndfollowed by the ( - ) key. This calls up the previous answer displayed on your screen. So “Ans” is short for “Answer.” Redo Example 9 using “Ans” feature. Example 10: A ball is tossed upward from a building, and its upward velocity, V, in feet per second, is a function of the time t, in seconds, since the ball was thrown. The formula for this is (????) = 40 − 32???? . This function ignores air resistance. The function is positive when the ball is rising and negative when the ball is falling. a. Find the velocity one second after the ball is thrown. Is the ball rising or falling then? b. Find the velocity two seconds after the ball is thrown. Is the ball rising or falling then? c. What is happening 1.25 seconds after the ball is thrown? d. By how much does the velocity change from 1 second to 2 seconds? From 2 seconds to 3 seconds? From 3 seconds to 4 seconds? What does this mean? Example 11: Example 16: The number ???? of deer present at time ???? (representing the number of years since the herd was introduced) on a certain wildlife refuge is given by the function 12.36 ???? ???? = ???? 0.03 + 0.55 a. What does ????(0) represent? Calculate its value. b. How many deer would you expect to be on the reserve 5 years after the herd is introduced? Ten years? Fifteen years? Twenty years? c. How much increase in the deer population would you expect from the 10 thto the 15th year?


Buy Material

Are you sure you want to buy this material for

0 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

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

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Jennifer McGill UCSF Med School

"Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over $500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"


"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


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


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:

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

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.