The columns below represent a function.
Input 20, -6, -10, 5, -2, -17, 8, ____
Output -2 7, -3, -3, 12, 5, 2, 9
Which numbers below an be placed on the blank line so that the table continues to represents a function? Select all that apply Show your work
a) -17
b) -8
c) -2
d) 2
e) 5
f) 8
g) 15
To determine which numbers can be placed on the blank line so that the table continues to represent a function, we need to make sure that each input value has a unique corresponding output value.
Looking at the given table, we can see that the input value -2 already has an output value of 12. Therefore, if we were to put another -2 in the input column, it would create a duplicate input value, which violates the definition of a function. So, we can eliminate -2 as a possible option.
Now, let's check the remaining options:
a) -17: This number could be a possible option because it is not currently in the input column.
b) -8: This number could be a possible option because it is not currently in the input column.
c) -2: We have already determined that -2 cannot be placed on the blank line because it would create a duplicate input value.
d) 2: This number could be a possible option because it is not currently in the input column.
e) 5: This number could be a possible option because it is not currently in the input column.
f) 8: This number could be a possible option because it is not currently in the input column.
g) 15: This number could be a possible option because it is not currently in the input column.
From the remaining options, we can select all that apply: a) -17, b) -8, d) 2, e) 5, f) 8, g) 15.
Numbers a) -17, e) 5, f) 8 are numbers you said could not be a possible option because they are not currently in the input column. When in fact they are in the input column. So what numbers can be placed on the blank line so the table continues to represent a function?
I apologize for the mistake in my previous response. You are correct, a) -17, e) 5, and f) 8 are already in the input column and cannot be placed on the blank line without creating a duplicate input value.
Looking at the remaining options:
b) -8: This number could be a possible option because it is not currently in the input column.
c) -2: This number cannot be placed on the blank line because it would create a duplicate input value.
d) 2: This number could be a possible option because it is not currently in the input column.
g) 15: This number could be a possible option because it is not currently in the input column.
Therefore, the numbers that can be placed on the blank line so that the table continues to represent a function are b) -8, d) 2, and g) 15.
Can you show your work.
Apologies for the oversight. Let's go through it again and show the work:
Given:
Input: 20, -6, -10, 5, -2, -17, 8
Output: -2, 7, -3, -3, 12, 5, 2, 9
We are looking for a number that can be placed on the blank line so that the table continues to represent a function.
Let's check each option:
a) -17: This number is already in the input column, so it cannot be placed on the blank line to avoid a duplicate input value.
b) -8: This number is not in the input column, so it is a possible option.
c) -2: This number is already in the input column, so it cannot be placed on the blank line to avoid a duplicate input value.
d) 2: This number is not in the input column, so it is a possible option.
e) 5: This number is already in the input column, so it cannot be placed on the blank line to avoid a duplicate input value.
f) 8: This number is already in the input column, so it cannot be placed on the blank line to avoid a duplicate input value.
g) 15: This number is not in the input column, so it is a possible option.
Therefore, the numbers that can be placed on the blank line so that the table continues to represent a function are b) -8, d) 2, and g) 15.