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.

Move to the left of .

Move to the left of .

Move to the left of .

Solve for in the first equation.

Rewrite the equation as .

Subtract from both sides of the equation.

Replace all occurrences of with in each equation.

Replace all occurrences of in with .

Replace all occurrences of in with .

Simplify each equation.

Remove parentheses.

Subtract from .

Remove parentheses.

Subtract from .

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 .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Move the negative in front of the fraction.

Replace all occurrences of with in each equation.

Replace all occurrences of in with .

Replace all occurrences of in with .

Simplify.

Simplify .

Simplify each term.

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Add and .

Simplify .

Cancel the common factor of .

Move the leading negative in into the numerator.

Cancel the common factor.

Rewrite the expression.

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 .

Simplify each term.

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

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 .

Cancel the common factor of .

Move the leading negative in into the numerator.

Cancel the common factor.

Rewrite the expression.

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 .

Simplify each term.

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

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 each term.

Raise to the power of .

Move to the left of .

Move to the left of .

Simplify each term.

Raise to the power of .

Move to the left of .

Move to the left of .

Simplify each term.

Raise to the power of .

Move to the left of .

Move to the left of .

Solve for in the first 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.

Replace all occurrences of with in each equation.

Replace all occurrences of in with .

Replace all occurrences of in with .

Simplify each equation.

Remove parentheses.

Simplify .

Subtract from .

Subtract from .

Remove parentheses.

Simplify .

Subtract from .

Subtract from .

Solve for in the second equation.

Rewrite the equation as .

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

Add to both sides 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 .

Simplify each term.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Move the negative in front of the fraction.

Replace all occurrences of with in each equation.

Replace all occurrences of in with .

Replace all occurrences of in with .

Simplify each equation.

Simplify .

Simplify each term.

Apply the distributive property.

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Multiply by .

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 .

Subtract from .

Simplify .

Simplify each term.

Apply the distributive property.

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Multiply by .

Move the negative in front of the fraction.

Add and .

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 .

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.

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 .

Subtract from .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify .

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Simplify the expression.

Multiply by .

Move the negative in front of the fraction.

Replace all occurrences of with in each equation.

Replace all occurrences of in with .

Replace all occurrences of in with .

Simplify.

Simplify .

Multiply .

Multiply by .

Combine and .

Multiply by .

Combine the numerators over the common denominator.

Add and .

Divide by .

Simplify .

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

Multiply .

Multiply and .

Multiply by .

Multiply .

Multiply by .

Multiply by .

Combine the numerators over the common denominator.

Subtract from .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

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.

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 .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Simplify by adding and subtracting.

Subtract from .

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 .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Move the leading negative in into the numerator.

Cancel the common factor.

Rewrite the expression.

Simplify by adding and subtracting.

Subtract from .

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 .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Simplify by adding and subtracting.

Subtract from .

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],[6,6],[3,8],[9,12]]