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 .

Add and .

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.

Solve for in the second equation.

Rewrite the equation as .

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

Subtract from .

Replace all occurrences of in with .

Simplify .

Multiply by .

Add and .

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 .

Add and .

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 .

Add and .

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 .

Add and .

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

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 .

Add and .

Add and .

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 .

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

Subtract from both sides of the equation.

Subtract from .

Replace all occurrences of in with .

Simplify .

Simplify each term.

Apply the distributive property.

Multiply by .

Multiply by .

Simplify by adding terms.

Add and .

Add and .

Solve for in the third equation.

Rewrite the equation as .

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

Subtract from .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Dividing two negative values results in a positive value.

Replace all occurrences of in with .

Simplify .

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

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 .

Simplify by adding zeros.

Add and .

Add and .

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 .

Combine fractions.

Combine fractions with similar denominators.

Simplify the expression.

Add and .

Divide by .

Add and .

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.

Raise to the power of .

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Simplify by adding numbers.

Add and .

Add and .

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.

The function is quadratic

The function is quadratic

The function is quadratic

Since all , the function is quadratic and follows the form .

Find the Function Rule table[[x,y],[0,3],[1,6],[2,12]]