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Precalculus : Relations and Functions

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Example Questions

Example Question #1 : 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 $\small (a,b)$ is true whenever $\small b$ is the child of $\small a$ . 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.

(Laksmi,Adriana) does not hold because Adriana is not Laksmi's child.

The relation is not a function because (Laksmi,Juan) and (Laksmi,Oksana) both hold.

(Adriana,Laksmi) does not hold because Laksmi is not Adriana's child and is a boy.

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.

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Example Question #3 : Determine If A Relation Is A Function

Which of the following relations is not a function?

Possible Answers:

y=2

x = y^2

$y = x^{\frac{3}{2}}$

$y = \sqrt{x}$

Correct answer:

x = y^2

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 x = y^2 , each value of corresponds to two values of (for example, when x = 4 , both y=2 and y = -2 are correct solutions). Therefore, this relation cannot be a function.

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Example Question #2 : Determine If A Relation Is A Function

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

(0,2)

(1,4)

(2,6)

(3,8)

(2,5)

Possible Answers:

Cannot be determined

Yes

Correct answer:

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.

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Example Question #1 : Determine If A Relation Is A Function

What equation is perpendicular to $y = \frac{5}{2}x+12$ and passes throgh (2,5) ?

Possible Answers:

$y = -\frac{5}{2}x + \frac{22}{5}$

$y = -\frac{2}{5}x + \frac{29}{5}$

$y = -\frac{4}{5}x + \frac{26}{5}$

$y = \frac{2}{5}x + \frac{21}{5}$

$y = -\frac{2}{5}x + \frac{27}{5}$

Correct answer:

$y = -\frac{2}{5}x + \frac{29}{5}$

Explanation:

First find the reciprocal of the slope of the given function.
$m_2 = -\frac{1}{m_1}$

$m_2 = -\frac{2}{5}$

The perpendicular function is:

$y = -\frac{2}{5}x+c$

Now we must find the constant, , by using the given point that the perpendicular crosses.

$5 = -\frac{2}{5}(2)+c$

solve for :

$c = \frac{29}{5}$

$y = -\frac{2}{5}x + \frac{29}{5}$

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Example Question #5 : Determine If A Relation Is A Function

Is the following relation of ordered pairs a function?

(1,1); (2,2); (3,1); (4,2); (5,1); (6,7)

Possible Answers:

Yes

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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Precalculus : Relations and Functions

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Determine If A Relation Is A Function

Example Question #3 : Determine If A Relation Is A Function

Example Question #2 : Determine If A Relation Is A Function

Example Question #1 : Determine If A Relation Is A Function

Example Question #5 : Determine If A Relation Is A Function

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