Question

multiple choice. choose the one alternative that best completes the statement or answers the question.
decide whether the relation is a function.

1. {(-5, -2), (-1, 1), (3, -6), (8, 1)}

a) function
b) not a function

1. {(2, -9), (2, -2), (6, 8), (8, 1), (11, -7)}

a) not a function
b) function

1. {(-8, 2), (-8, 8), (-1, 6), (4, 7), (7, 5)}

a) function
b) not a function
determine whether the relation is a function.
4)

a) function
b) not a function
5)

a) function
b) not a function
short answer. write the word or phrase that best completes each statement or answers the question.
determine whether the relation is a function. respond either \function\ or
ot a function\. if it is not a function then state what is wrong in the relation that prevents it from being a function.
6)

multiple choice. choose the one alternative that best completes the statement or answers the question.
determine whether the relation is a function.
7)

a) function
b) not a function

Explanation:

Step1: Recall the definition of a function

A relation is a function if for each input (first element of the ordered pair or the left - hand side of the mapping), there is exactly one output (second element of the ordered pair or the right - hand side of the mapping).

Step2: Analyze each relation

• For relation 1: \(\{(-5,-2),(-1,1),(3,-6),(8,1)\}\)

Each \(x\) - value (\(-5\), \(-1\), \(3\), \(8\)) has exactly one \(y\) - value.

• For relation 2: \(\{(2,-9),(2,-2),(6,8),(8,1),(11,-7)\}\)

The \(x\) - value \(2\) has two different \(y\) - values (\(-9\) and \(-2\)).

• For relation 3: \(\{(-8,2),(-8,8),(-1,6),(4,7),(7,5)\}\)

The \(x\) - value \(-8\) has two different \(y\) - values (\(2\) and \(8\)).

• **For relation 4: Mapping \(

$$\begin{cases}a\to x\\b\to y\\c\to z\end{cases}$$

\)**
Each input (\(a\), \(b\), \(c\)) has exactly one output (\(x\), \(y\), \(z\)).

• **For relation 5: Mapping \(

$$\begin{cases}1\to - 15\\-6\to15\\-16\to - 7\end{cases}$$

\)**
Each input (\(1\), \(-6\), \(-16\)) has exactly one output (\(-15\), \(15\), \(-7\)).

• For relation 6: \(x=-6\) (vertical line \(x = - 6\))

For \(x=-6\), there are infinitely many \(y\) - values.

• **For relation 7: Mapping \(

$$\begin{cases}9\to - 17\\-10\to19\\-15\to - 10\end{cases}$$

\)**
Each input (\(9\), \(-10\), \(-15\)) has exactly one output (\(-17\), \(19\), \(-10\)).

Answer:

1. A. Function
2. A. Not a function
3. B. Not a function
4. A. Function
5. A. Function
6. Not a function. A vertical line \(x = - 6\) fails the vertical line test (for \(x=-6\), there are infinitely many \(y\) - values).
7. A. Function