To fill in the missing values in the table, we can start by substituting the given values of x into the equation and solving for y.
Let's start with the given value x = 1:
Substituting x = 1 into the equation y - 5 = x^3:
y - 5 = 1^3
y - 5 = 1
Adding 5 to both sides of the equation:
y = 1 + 5
y = 6
So, when x = 1, y = 6.
Next, let's substitute the given value x = -3:
Substituting x = -3 into the equation y - 5 = x^3:
y - 5 = (-3)^3
y - 5 = -27
Adding 5 to both sides of the equation:
y = -27 + 5
y = -22
So, when x = -3, y = -22.
Now, let's move on to the remaining values.
For x = 0:
Substituting x = 0 into the equation y - 5 = x^3:
y - 5 = 0^3
y - 5 = 0
Adding 5 to both sides of the equation:
y = 0 + 5
y = 5
So, when x = 0, y = 5.
For x = 6:
Substituting x = 6 into the equation y - 5 = x^3:
y - 5 = 6^3
y - 5 = 216
Adding 5 to both sides of the equation:
y = 216 + 5
y = 221
So, when x = 6, y = 221.
For x = 8:
Substituting x = 8 into the equation y - 5 = x^3:
y - 5 = 8^3
y - 5 = 512
Adding 5 to both sides of the equation:
y = 512 + 5
y = 517
So, when x = 8, y = 517.
Now, we can fill in the missing values in the table:
x y
1 6
-3 -22
0 5
6 221
8 517