# Find the Function Rule table[[x,y],[0,0],[1,-2],[2,0]] Check if the function rule is linear.
To find if the table follows a function rule, check to see if the values follow the linear form .
Build a set of equations from the table such that .
Calculate the values of and .
Simplify each equation.
Simplify .
Multiply by .
Multiply by .
Move to the left of .
Rewrite the equation as .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Replace all occurrences of in with .
Simplify.
Remove parentheses.
Remove parentheses.
Rewrite the equation as .
Replace all occurrences of in with .
Multiply by .
Since , there are no solutions.
No solution
No solution
Calculate the value of using each value in the relation and compare this value to the given value in the relation.
Calculate the value of when , , and .
Multiply by .
If the table has a linear function rule, for the corresponding value, . This check passes since and .
Calculate the value of when , , and .
Multiply by .
If the table has a linear function rule, for the corresponding value, . This check passes since and .
Calculate the value of when , , and .
Multiply by .
If the table has a linear function rule, for the corresponding value, . This check does not pass, since and . The function rule can’t be linear.
Since for the corresponding values, the function is not linear.
The function is not linear
The function is not linear
The function is not linear
Check if the function rule is quadratic.
To find if the table follows a function rule, check whether the function rule could follow the form .
Build a set of equations from the table such that .
Calculate the values of , , and .
Simplify each equation.
Simplify .
Simplify each term.
Raising to any positive power yields .
Multiply by .
Multiply by .
Combine the opposite terms in .
Simplify each term.
One to any power is one.
Multiply by .
Multiply by .
Simplify each term.
Raise to the power of .
Move to the left of .
Move to the left of .
Rewrite the equation as .
Replace all occurrences of with in each equation.
Replace all occurrences of in with .
Replace all occurrences of in with .
Simplify.
Remove parentheses.
Remove parentheses.
Solve for in the second equation.
Rewrite the equation as .
Subtract from both sides of the equation.
Replace all occurrences of in with .
Simplify .
Simplify each term.
Apply the distributive property.
Multiply by .
Multiply by .
Solve for in the third equation.
Rewrite the equation as .
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Replace all occurrences of in with .
Simplify .
Multiply by .
Calculate the value of using each value in the table and compare this value to the given value in the table.
Calculate the value of such that when , , , and .
Simplify each term.
Raising to any positive power yields .
Multiply by .
Multiply by .
If the table has a quadratic function rule, for the corresponding value, . This check passes since and .
Calculate the value of such that when , , , and .
Simplify each term.
One to any power is one.
Multiply by .
Multiply by .
Simplify by subtracting numbers.
Subtract from .
If the table has a quadratic function rule, for the corresponding value, . This check passes since and .
Calculate the value of such that when , , , and .
Simplify each term.
Multiply by by adding the exponents.
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Raise to the power of .
Multiply by .
Simplify by subtracting numbers.
Subtract from .
If the table has a quadratic function rule, for the corresponding value, . This check passes since and .
Since for the corresponding values, the function is quadratic.     