Precalculus : Relations and Functions

Study concepts, example questions & explanations for Precalculus

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Example Questions

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Example Question #3 : 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?

Possible Answers:

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.

(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.

Correct answer:

Even if the two parents had only one daughter, the relation would not be a function.

Explanation:

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 #4 : Determine If A Relation Is A Function

Which of the following relations is not a function?

Possible Answers:

Correct answer:

Explanation:

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 #5 : Determine If A Relation Is A Function

Given the set of ordered pairs, determine if the relation is a function

Possible Answers:

Cannot be determined

No

Yes

Correct answer:

No

Explanation:

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 #6 : Determine If A Relation Is A Function

What equation is perpendicular to  and passes throgh ?

Possible Answers:

Correct answer:

Explanation:

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 :

Example Question #7 : Determine If A Relation Is A Function

Is the following relation of ordered pairs a function? 

 

 

Possible Answers:

Yes

No

Cannot be determined

Correct answer:

Yes

Explanation:

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.

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