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Example Questions
Example Question #3 : Determine If A Relation Is A Function
Is the following relation of ordered pairs a function?
Cannot be determined
No
Yes
Yes
A set of ordered pairs is a function if it passes the vertical line test.
Because there are no more than one corresponding value for any given
value, the relation of ordered pairs IS a function.
Example Question #1 : Define A Field
Which of the following is not true about a field. (Note: the real numbers is a field)
There is an element in the field such that
for any element
in the field.
For every element in the field, there is another element
such that their product
is equal to
, where
is the multiplicative identity,
in the case of real numbers.
A field can be defined in many ways.
For every element in the field, there is another element
such that their sum
is equal to
, where
is the additive identity.
We have for any
and
in the field.
For every element in the field, there is another element
such that their product
is equal to
, where
is the multiplicative identity,
in the case of real numbers.
It is not the case that for any element in a field, there is another one
such that their product is
. Take
in the real numbers. Multiply
by any number and you get
, so you will never get
. This is true for any field that has more than 1 element.
Example Question #1 : Modeling
John lives in Atlanta, but commutes every Monday to LaGrange where he has an apartment he stays in Monday-Friday for work. Each Monday he drives 350 miles to LaGrange. Once he arrives to his home away from home he is in walking distance of work and does not use his car for anything else. After 23 weeks his odometer shows 186,000 miles. Write an equation that models his odometer reading as a function of the number of weeks he has been driving after commencing his new job.
The rate of change of his mileage is 700 per week (350 x 2=700 there and back). The rate of change is the same thing as slope. Since we are looking for equation an equation that models his odometer reading as a function of the number of weeks he has been driving we can extract the point (23 , 18600) since after 23 weeks his odometer read 18,600 miles. Now we will use the point slope formula:
distribute the right side
isolate y
Example Question #1 : Modeling
John lives in Atlanta, but commutes every Monday to LaGrange where he has an apartment he stays in Monday-Friday. Each Monday he drives 350 miles to LaGrange. Once he arrives to his apartment he is in walking distance of work and does not use his car for anything else. After 23 weeks his odometer shows 186,000 miles. Write an equation that models his odometer reading as a function of the number of weeks he has been driving after commencing his new job. Using the equation you just made, what is the y intercept or his original mileage before starting?
Need more information to solve.
y intercept=169,900 miles
y intercept=186,000 miles
y intercept=153,800 miles
y intercept=16,100 miles
y intercept=169,900 miles
The y intercept can be found by plugging in 0 for x in your original equation: y=700x+169,900 because at x=0 you can only reach the y axis and thus will find the y intercept.
Example Question #1 : Inverse Functions
What is the inverse function of
?
To find the inverse function of
we replace the with
and vice versa.
So
Now solve for
Example Question #2 : Find The Inverse Of A Relation
Find the inverse of the function.
To find the inverse function, first replace with
:
Now replace each with an
and each
with a
:
Solve the above equation for :
Replace with
. This is the inverse function:
Example Question #2 : Linear Algebra
Find the inverse of the function.
To find the inverse function, first replace with
:
Now replace each with an
and each
with a
:
Solve the above equation for :
Replace with
. This is the inverse function:
Example Question #3 : Find The Inverse Of A Relation
Find the inverse of the function .
To find the inverse of , interchange the
and
terms and solve for
.
Example Question #1 : Find The Inverse Of A Relation
What point is the inverse of the ?
When trying to find the inverse of a point, switch the x and y values.
So
Example Question #2 : Find The Inverse Of A Relation
What is the inverse of ?
When trying to find the inverse of a point, switch the x and y values.
So,
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