Engineering Mathematics Exam > Engineering Mathematics Videos > How to create a function from an equation (example) - Functions, Algebra I, Mathematics
How to create a function from an equation (example) - Functions, Algebra I, Mathematics Video Lecture - Engineering Mathematics
FAQs on How to create a function from an equation (example) - Functions, Algebra I, Mathematics Video Lecture - Engineering Mathematics
| 1. How do you create a function from an equation? |  |
| 2. Can any equation be converted into a function? | |
Ans. Not all equations can be converted into functions. For an equation to be considered a function, each value of the independent variable must correspond to exactly one value of the dependent variable. In other words, there should be no multiple y-values for a single x-value. Equations that fail to meet this criteria, such as those with multiple y-values for a single x-value, cannot be converted into functions.
| 3. How do you determine the domain and range of a function created from an equation? | |
Ans. To determine the domain and range of a function created from an equation, you need to analyze the restrictions on both the independent and dependent variables. The domain represents all possible values of the independent variable (x) for which the function is defined, while the range represents all possible values of the dependent variable (y) that the function can take. By analyzing the equation, you can identify any restrictions or limitations on x and y, which will help determine the domain and range of the function.
| 4. Are all functions created from equations linear in nature? | |
Ans. No, not all functions created from equations are linear in nature. While linear functions are one type of function, there are various other types as well, such as quadratic, exponential, logarithmic, trigonometric, and many more. The type of function created from an equation depends on the relationship between the dependent and independent variables as defined by the equation.
| 5. Can functions created from equations be used to solve real-world problems? | |
Ans. Yes, functions created from equations are often used to solve real-world problems. By representing real-world situations mathematically, equations can be transformed into functions that can then be analyzed and used to make predictions or solve problems. For example, functions can be used to model population growth, determine optimal solutions in engineering problems, or predict future trends based on existing data.
Text Transcript from Video
For a given input value b, the function
f outputs a value a to satisfy the
following equation 4a plus 7b
is equal to negative 52. So for a given input b,
the function f, the function f
will
output an a that satisfies this
relationship right over here for the a
and the b. Write a formula for f of b
in terms of b. So we want to do,
we just want to solve for --
if we're given a "b", what "a" does that
imply that we have to
output? Or another way to think about it is
-- let's just solve for
a, or we could think about a as being a
function of
b. So let's write this. So we have 4a
plus 7b -- is equal to
negative 52. So I can solve for a
in terms of b, that any b that I have --
Let's say these b's are on the right hand side I
can
put it in. I can substitute that value
for b and I can just solve for a.
I can solve for a that needs to be
outputted.
So let's do that. Let's solve for a.
So I want to get all the a on
I wanna just have an a leftover on the
left hand side, and have everything else on
the right hand side including the b's.
So let's get rid of this b on the left hand
side. And
I can do that by subtracting 7b.
Of course I wanna do that to both sides.
I can't just do an equation and
do an operation only on one side like
that. So
let's subtract, and we are left with
we are left with --
the 7b's add up to zero. 7b minus 7b.
We're left with
4a is equal to negative 52
minus 7b, minus
7b. Now, to isolate the a here,
just to have an a here instead of 4a,
we can divide both sides by 4. We can
divide both sides by 4. So I'm gonna
divide everything
by 4. And on the left hand side, we got
our goal.
We are left with an a is equal to -- Now
what's negative 54 divided by --
What is the negative 52 divided by 4?
So let's think about it.
52 is 40 plus 12. 40 divided by
4 is 10. 12 divided by
4 is 3. So it's gonna be 13. Negative 13.
So it's negative
13 minus 7/4 b
minus 7/4 b. So
given a "b", if you give me a "b", I can put
that value right over here,
and I can calculate what the
corresponding a needs to be
in order to satisfy this relationship.
So if I want a formula for f of b in
terms of b, I can say, look,
you give me a "b", the output of our
function, which is
f of a. The output of our function is
going to be --
is going to be negative 13 minus
7/4 b, because the output of our
function needs to be an
"a" that will satisfy -- that will satisfy
this equation up here.
So hopefully that helped.
f outputs a value a to satisfy the
following equation 4a plus 7b
is equal to negative 52. So for a given input b,
the function f, the function f
will
output an a that satisfies this
relationship right over here for the a
and the b. Write a formula for f of b
in terms of b. So we want to do,
we just want to solve for --
if we're given a "b", what "a" does that
imply that we have to
output? Or another way to think about it is
-- let's just solve for
a, or we could think about a as being a
function of
b. So let's write this. So we have 4a
plus 7b -- is equal to
negative 52. So I can solve for a
in terms of b, that any b that I have --
Let's say these b's are on the right hand side I
can
put it in. I can substitute that value
for b and I can just solve for a.
I can solve for a that needs to be
outputted.
So let's do that. Let's solve for a.
So I want to get all the a on
I wanna just have an a leftover on the
left hand side, and have everything else on
the right hand side including the b's.
So let's get rid of this b on the left hand
side. And
I can do that by subtracting 7b.
Of course I wanna do that to both sides.
I can't just do an equation and
do an operation only on one side like
that. So
let's subtract, and we are left with
we are left with --
the 7b's add up to zero. 7b minus 7b.
We're left with
4a is equal to negative 52
minus 7b, minus
7b. Now, to isolate the a here,
just to have an a here instead of 4a,
we can divide both sides by 4. We can
divide both sides by 4. So I'm gonna
divide everything
by 4. And on the left hand side, we got
our goal.
We are left with an a is equal to -- Now
what's negative 54 divided by --
What is the negative 52 divided by 4?
So let's think about it.
52 is 40 plus 12. 40 divided by
4 is 10. 12 divided by
4 is 3. So it's gonna be 13. Negative 13.
So it's negative
13 minus 7/4 b
minus 7/4 b. So
given a "b", if you give me a "b", I can put
that value right over here,
and I can calculate what the
corresponding a needs to be
in order to satisfy this relationship.
So if I want a formula for f of b in
terms of b, I can say, look,
you give me a "b", the output of our
function, which is
f of a. The output of our function is
going to be --
is going to be negative 13 minus
7/4 b, because the output of our
function needs to be an
"a" that will satisfy -- that will satisfy
this equation up here.
So hopefully that helped.
Related Exams
About this Video
Apr 12, 2025
Last updated
How to create a function from an equation (example) - Functions, Algebra I, Mathematics for Engineering Mathematics 2025 is part of Engineering Mathematics preparation. The notes and questions for How to create a function from an equation (example) - Functions, Algebra I, Mathematics
have been prepared according to the Engineering Mathematics exam syllabus. Information about How to create a function from an equation (example) - Functions, Algebra I, Mathematics covers all important topics
for Engineering Mathematics 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises
and tests below for How to create a function from an equation (example) - Functions, Algebra I, Mathematics.
Introduction of How to create a function from an equation (example) - Functions, Algebra I, Mathematics in English is available as part of our Engineering Mathematics preparation & How to create a function from an equation (example) - Functions, Algebra I, Mathematics in Hindi
for Engineering Mathematics courses. Download more important topics, notes, lectures and mock test series for Engineering Mathematics Exam by
signing up for free.
Description
Video Lecture & Questions for How to create a function from an equation (example) - Functions, Algebra I, Mathematics Video Lecture - Engineering Mathematics - Engineering Mathematics full syllabus preparation | Free video for Engineering Mathematics exam.
Information about How to create a function from an equation (example) - Functions, Algebra I, Mathematics
Here you can find the How to create a function from an equation (example) - Functions, Algebra I, Mathematics defined & explained in the simplest way possible. Besides explaining types of How to create a function from an equation (example) - Functions, Algebra I, Mathematics
theory, EduRev gives you an ample number of questions to practice How to create a function from an equation (example) - Functions, Algebra I, Mathematics tests, examples and also practice Engineering Mathematics tests.
Related Searches
Summary
,Mathematics Video Lecture - Engineering Mathematics
,Exam
,practice quizzes
,How to create a function from an equation (example) - Functions
,Semester Notes
,How to create a function from an equation (example) - Functions
,Objective type Questions
,study material
,Free
,mock tests for examination
,Previous Year Questions with Solutions
,video lectures
,past year papers
,Algebra I
,Mathematics Video Lecture - Engineering Mathematics
,Extra Questions
,Algebra I
,Sample Paper
,Algebra I
,ppt
,Viva Questions
,Mathematics Video Lecture - Engineering Mathematics
,shortcuts and tricks
,Important questions
,How to create a function from an equation (example) - Functions
,MCQs
;
Study How to create a function from an equation (example) - Functions, Algebra I, Mathematics on the App
Students of Engineering Mathematics can study How to create a function from an equation (example) - Functions, Algebra I, Mathematics alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the How to create a function from an equation (example) - Functions, Algebra I, Mathematics,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of How to create a function from an equation (example) - Functions, Algebra I, Mathematics is prepared as per the latest Engineering Mathematics syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup