Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

input output independent variable dependent variable, Summaries of Calculus for Engineers

University of Washington (UW) - SeattleCalculus for Engineers

A function is a relationship from one element to another. Domain is the set of all inputs to a function. Range is the set of all outputs of a function. Note: ...

Typology: Summaries

2022/2023

Uploaded on 03/01/2023

anasooya
anasooya 🇺🇸

4.1

(13)

244 documents

1 / 4

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
3.1 Functions
A function is a relationship from one element to another.
Basically a special type of equation
Definitions:
For a function f(x)=y,
Names for x Names for f(x) (or y)
input output
independent variable dependent variable
Domain is the set of all inputs to a function.
Range is the set of all outputs of a function.
Note: Each input can only go to one output!
Ex. Are these functions?
𝑓(𝑥)= 𝑥 + 2 𝑥+ 𝑦= 9
𝑦 = 𝑥 𝑥𝑦 = 4
pf3
pf4

Partial preview of the text

Download input output independent variable dependent variable and more Summaries Calculus for Engineers in PDF only on Docsity!

A function is a relationship from one element to another.

Basically a special type of equation

Definitions:

For a function f(x)=y,

Names for x Names for f(x) (or y)

input output

independent variable dependent variable

Domain is the set of all inputs to a function.

Range is the set of all outputs of a function.

Note: Each input can only go to one output!

Ex. Are these functions?

ଶ

ଶ

ଶ

We can also use explicit form to see if an equation is a function.

The previous examples without f(x) were in implicit form.

Ex. Put these equations in explicit form, or write “not a function.”

ଶ

ଶ

ଶ

Finding Domain

1. Start with all real numbers.

2. Is there a variable in the denominator? If there is, exclude the values

that make the denominator zero.

3. Is there an even radical (square root, ¼ power, etc.) of a

variable? If there is, exclude the values that make it negative under the

radical.

Operations of Functions

Addition (sum):

Subtraction (difference):

Multiplication (product):

Division (quotient):

Ex. Find the sum, difference, product, and quotient of 𝑓

= 𝑥 − 1 and 𝑔

ଶ

. Also give the domain of each.

Now evaluate all of those at x=3.