Jerome is constructing a table of values that satisfies the definition of a function. Input -11 -4 0 3 5 7 12 Output -15 -11 -9 -2 -1 5 5 13 ​Which number(s) can be placed in the empty cell so that the table of values satisfies the definition of a function? ​Select all that apply. (2 points) Responses -5 -5 -1 -1 0 0 3 3 7 7 17

Answer 1

To determine which number(s) can be placed in the empty cell in Jerome's table, we need to ensure that each input corresponds to exactly one output, as per the definition of a function.

The pairs of input and output values that we have are as follows:

• Input -11 corresponds to Output -15
• Input -4 corresponds to Output -11
• Input 0 corresponds to Output -9
• Input 3 corresponds to Output -2
• Input 5 corresponds to Output -1
• Input 7 corresponds to Output 5
• Input 12 corresponds to Output 13

From the given table, we see that the current mappings of inputs to outputs are unique. To maintain this unique mapping, we must avoid repeating outputs for any of the current inputs.

Now let's analyze the provided response options to find out which number(s) can be used as an output for the empty input without violating the function's definition:

Options to choose from:

• -5: Not used, valid option.
• -1: Already associated with the input 5, invalid option.
• 0: Not used, valid option.
• 3: Not used, valid option.
• 7: Not used, valid option.
• 17: Not used, valid option.

Thus, the numbers that can be placed in the empty cell without repeating an output for an existing input are:

• -5
• 0
• 3
• 7
• 17

Final selection of valid outputs: -5, 0, 3, 7, 17.