Engineering Mathematics Exam > Engineering Mathematics Videos > Recognizing functions (example 5)
Recognizing functions (example 5) Video Lecture - Engineering Mathematics
FAQs on Recognizing functions (example 5) Video Lecture - Engineering Mathematics
| 1. What is a function in engineering mathematics? |  |
Ans. A function in engineering mathematics is a relation between a set of inputs and a set of outputs, where each input is uniquely associated with exactly one output. It is commonly represented as f(x) and is used to describe the relationship between variables in engineering problems.
| 2. How do you recognize a function in engineering mathematics? | |
Ans. To recognize a function in engineering mathematics, you need to check if each input value has a unique output value. This means that for every value of x, there should be only one corresponding value of f(x). If there are multiple outputs for a single input, then it is not a function.
| 3. What are the different types of functions in engineering mathematics? | |
Ans. There are several types of functions in engineering mathematics, including linear functions, quadratic functions, trigonometric functions, exponential functions, logarithmic functions, and many more. Each type of function has its own unique characteristics and applications in engineering.
| 4. How can functions be represented graphically in engineering mathematics? | |
Ans. Functions in engineering mathematics can be represented graphically by plotting the input values along the x-axis and the corresponding output values along the y-axis. This creates a graph that visually shows the relationship between the variables. The shape and behavior of the graph provide valuable insights into the properties of the function.
| 5. What is the importance of recognizing functions in engineering mathematics? | |
Ans. Recognizing functions in engineering mathematics is crucial because it helps in understanding and analyzing the relationships between variables in engineering problems. It allows engineers to model real-world phenomena, make predictions, solve equations, and optimize systems. Without recognizing functions, it would be challenging to analyze and solve complex engineering problems efficiently.
Text Transcript from Video
Jada is ordering Mother's
Day gifts online.
The shipping costs are based on
the dollar amount of the order.
For orders less than
$20, shipping costs $4.
For orders $20 or
more, shipping is $7.
Can the dollar
amount of the order
be represented as a
function of shipping costs?
So they're saying,
can the dollar amount
of the order-- so can
the amount of order
be represented as a
function of shipping--
let me do that in
that blue color costs.
So if we have the shipping
costs as an input,
will that map to exactly--
for a given input,
will we get exactly one output
for the amount of order?
In order for this to be
represented as a function,
we have to input a shipping
cost, a shipping cost
where this relationship
is defined.
We need to input
a shipping cost,
put it into our relationship,
and get exactly one dollar
amount of the order in order
for this to be a function.
If we get multiple dollar
amounts of the order, then
the relationship, well,
it's still a relationship,
but it's not going
to be a function.
So let's think about it.
What are the
possible inputs here?
Well, there's only two
possible shipping costs.
Shipping costs are
either going to be $4,
or they're going to be $7.
So let's think
about what happens
when we input $4 in
as a shipping cost.
So if we input $4
into our relationship,
so we input $4 into our
little potential function box,
so $4 into it,
what is the output?
What is going to be the
amount of the order?
Well, if the shipping cost is
$4, the amount of the order
just has to be
anything less than $20.
So it could have been $1.
It could have been $1.50.
It could've been $7.
It literally can take
on any value up to $20.
So it could even be $19.99.
We could do a similar
thing if we input 7
into this relationship.
If 7 was-- and I could put
literally an infinite number
of numbers.
It could be a million dollars.
So if I input 7 into
this relationship
that we're trying to test
whether it's a function, if 7
is the shipping costs,
then the order we just know
is over $20, $20 or more.
So it could be $20.
It could be $800.
It could be $1 million.
There's actually an
infinite number of values
that it could take
on right over here.
So because for a
valid shipping cost,
for each of these
valid shipping costs,
I can get many, many,
many potential outputs,
I don't know which output it
necessarily will output to.
If someone tells you
the shipping costs
and you don't necessarily
know what the order size was,
this is not a function.
You cannot represent the
amount of order as a function
of the shipping cost.
So, no.
Day gifts online.
The shipping costs are based on
the dollar amount of the order.
For orders less than
$20, shipping costs $4.
For orders $20 or
more, shipping is $7.
Can the dollar
amount of the order
be represented as a
function of shipping costs?
So they're saying,
can the dollar amount
of the order-- so can
the amount of order
be represented as a
function of shipping--
let me do that in
that blue color costs.
So if we have the shipping
costs as an input,
will that map to exactly--
for a given input,
will we get exactly one output
for the amount of order?
In order for this to be
represented as a function,
we have to input a shipping
cost, a shipping cost
where this relationship
is defined.
We need to input
a shipping cost,
put it into our relationship,
and get exactly one dollar
amount of the order in order
for this to be a function.
If we get multiple dollar
amounts of the order, then
the relationship, well,
it's still a relationship,
but it's not going
to be a function.
So let's think about it.
What are the
possible inputs here?
Well, there's only two
possible shipping costs.
Shipping costs are
either going to be $4,
or they're going to be $7.
So let's think
about what happens
when we input $4 in
as a shipping cost.
So if we input $4
into our relationship,
so we input $4 into our
little potential function box,
so $4 into it,
what is the output?
What is going to be the
amount of the order?
Well, if the shipping cost is
$4, the amount of the order
just has to be
anything less than $20.
So it could have been $1.
It could have been $1.50.
It could've been $7.
It literally can take
on any value up to $20.
So it could even be $19.99.
We could do a similar
thing if we input 7
into this relationship.
If 7 was-- and I could put
literally an infinite number
of numbers.
It could be a million dollars.
So if I input 7 into
this relationship
that we're trying to test
whether it's a function, if 7
is the shipping costs,
then the order we just know
is over $20, $20 or more.
So it could be $20.
It could be $800.
It could be $1 million.
There's actually an
infinite number of values
that it could take
on right over here.
So because for a
valid shipping cost,
for each of these
valid shipping costs,
I can get many, many,
many potential outputs,
I don't know which output it
necessarily will output to.
If someone tells you
the shipping costs
and you don't necessarily
know what the order size was,
this is not a function.
You cannot represent the
amount of order as a function
of the shipping cost.
So, no.
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Dec 26, 2024 Last updated |
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