which rule matches the functions shown in the table?
x y
-1 1
1 -1
2 -2
a. y=x+2
b. y= x-2
c. y= x-4
d. y= -x
The bot picked y = x - 2 and then proceeded to check:
Unfortunately all checks show that it picked the wrong equation
When x = -1, y = (-1) - 2 = -3. <------ should have been 1
When x = 1, y = (1) - 2 = -1. <------ should have been -1
When x = 2, y = (2) - 2 = 0. <------ should have been -2
so clearly the correct answer is
y = -x
This is weird :(
To determine which rule matches the functions shown in the table, we need to analyze the relationship between the values of x and y.
Let's start by examining the first row of the table:
x = -1, y = 1
If we substitute these values into each option, we get the following results:
Option a: y = (-1) + 2 = 1 + 2 = 3
Option b: y = (-1) - 2 = -3
Option c: y = (-1) - 4 = -5
Option d: y = -(-1) = 1
Based on the first row, the only option that matches is Option d: y = -x. But to confirm if this rule applies to all the values in the table, let's check the remaining two rows as well.
For the second row:
x = 1, y = -1
Option a: y = (1) + 2 = 3
Option b: y = (1) - 2 = -1
Option c: y = (1) - 4 = -3
Option d: y = -(1) = -1
Again, Option d matches with the second row.
Lastly, let's check the third row:
x = 2, y = -2
Option a: y = (2) + 2 = 4
Option b: y = (2) - 2 = 0
Option c: y = (2) - 4 = -2
Option d: y = -(2) = -2
Once again, we see that Option d matches with the third row.
Therefore, the rule that matches the functions shown in the table is Option d: y = -x.
Option (b) y = x - 2 matches the functions shown in the table.
When x = -1, y = (-1) - 2 = -3.
When x = 1, y = (1) - 2 = -1.
When x = 2, y = (2) - 2 = 0.
Therefore, the rule is y = x - 2.