Question

A function is a relation in which every input has exactly one output.

Which choice represents a function?


CLEAR CHECK

Inputs: negative 4, 5, 8, negative 5. Output: 4, 3, 9, negative 5). Negative 4 goes to 4 and 3. 5 goes to 3. 8 goes to 9. negative 5 goes to negative 5.

On a coordinate plane, a vertical line goes through x = 3.

A 2-column table with 7 rows. Column 1 is labeled x with entries 4, 3, 0, negative 8, 3, 4, 9. Column 2 is labeled y with entries 4, 2, negative 1, 7, negative 3, 5, 14.

(−3,4),(2,6),(0,3),(8,4)
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Answer 1

will find at bottom

Explanation:

A relation is a function of x if each value of x in the domain corresponds to exactly one value of y in the range. In other words, there should be no repeated values of x with different values of y.

Let's analyze each of the given tables to determine which one represents a function of x:

1. Table 1: In this table, we have x values of -1, 2, 2, and 3. Notice that x = 2 appears twice with different y values. This violates the definition of a function, so Table 1 is not a function of x.

2. Table 2: This table has x values of -8, -8, 1, and 1. Similar to the previous table, x = -8 and x = 1 appear twice with different y values. Therefore, Table 2 is not a function of x.

3. Table 3: In this table, all the x values are the same, which is -5. However, the corresponding y values are different (-9, 7, -9, and 2). Since each x value has a unique y value, Table 3 represents a function of x.

4. Table 4: This table consists of x values of -3, -2, 4, and 7. Each x value corresponds to a unique y value (-1, 5, 0, and -1). Therefore, Table 4 also represents a function of x.

To summarize, the relations that are functions of x are Table 3 and Table 4.

Answer 2

On a coordinate plane, a vertical line goes through x = 3.

Explanation:

I haven't looked at the other choices, but clearly this is a function