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Example Questions
Example Question #1021 : Pre Calculus
What is the domain of the function?
Does not exist anywhere.
Exponentials cannot have negatives on the inside. However, the expoential will convert any value into a positive value.
Example Question #52 : Relations And Functions
What is the domain of the function?
Looking at the denominator, the function cannot exist at . The natural log function cannot have a
or negative inside. Since the
value is raised to the power of
, any negative
value will be convert to a positive value. However, the function will not exist if the inside of the natural is
, where
.
will exist any where else.
Example Question #62 : Functions
What is the domain of the function?
The denominator becomes where
, and the inside of the natural log also becomes
at
. The function will not exist at these two points. The
value cannot be less than
, becuase that will leave a negative value inside in the natural log.
Example Question #62 : Functions
Find the domain of the function.
Simplify:
Even though the cancels out from the numerator and denominator, there is still a hole where the function discontinues at
. The function also does not exist at
, where the denominator becomes
.
Example Question #1 : Determine If A Relation Is A Function
Which of the following expressions is not a function?
Recall that an expression is only a function if it passes the vertical line test. Test this by graphing each function and looking for one which fails the vertical line test. (The vertical line test consists of drawing a vertical line through the graph of an expression. If the vertical line crosses the graph of the expression more than once, the expression is not a function.)
Functions can only have one y value for every x value. The only choice that reflects this is:
Example Question #51 : Relations And Functions
Suppose we have the relation on the set of real numbers
whenever
. Which of the following is true.
The relation is not a function because holds but
does not.
The relation is a function because holds and
also holds.
The relation is a function because every relation is a function, since that's how relations are defined.
The relation is not a function because and
both hold.
The relation is a function because for every , there is only one
such that
holds.
The relation is not a function because and
both hold.
The relation is not a function because and
hold. If it were a function,
would hold only for one
. But we know it holds for
because
and
. Thus, the relation
on the set of real numbers
is not a function.
Example Question #2 : Determine If A Relation Is A Function
Consider a family consisting of a two parents, Juan and Oksana, and their daughters Adriana and Laksmi. A relation is true whenever
is the child of
. Which of the following is not true?
Even if the two parents had only one daughter, the relation would not be a function.
(Adriana,Laksmi) does not hold because Laksmi is not Adriana's child and is a boy.
The relation is not a function because (Laksmi,Juan) and (Laksmi,Oksana) both hold.
(Laksmi,Adriana) does not hold because Adriana is not Laksmi's child.
If the two parents had only one daughter, the relation would be a function.
Even if the two parents had only one daughter, the relation would not be a function.
The statement
"Even if the two parents had only one daughter, the relation would not be a function."
is not true because if they had only one daughter, say Adriana, then the only relations that would exist would be (Juan, Adriana) and (Oksana,Adriana), which defines a function.
Example Question #3 : Determine If A Relation Is A Function
Which of the following relations is not a function?
The definition of a function requires that for each input (i.e. each value of ), there is only one output (i.e. one value of
). For
, each value of
corresponds to two values of
(for example, when
, both
and
are correct solutions). Therefore, this relation cannot be a function.
Example Question #2 : Determine If A Relation Is A Function
Given the set of ordered pairs, determine if the relation is a function
No
Yes
Cannot be determined
No
A relation is a function if no single x-value corresponds to more than one y-value.
Because the mapping from goes to
and
the relation is NOT a function.
Example Question #1 : Determine If A Relation Is A Function
What equation is perpendicular to and passes throgh
?
First find the reciprocal of the slope of the given function.
The perpendicular function is:
Now we must find the constant, , by using the given point that the perpendicular crosses.
solve for :
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