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 .

Simplify each term.

Move to the left of .

Rewrite as .

Solve for in the first equation.

Rewrite the equation as .

Add to 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.

Add and .

Remove parentheses.

Add and .

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 with in each equation.

Replace all occurrences of in with .

Replace all occurrences of in with .

Simplify.

Simplify .

Multiply by .

Subtract from .

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 .

Subtract from .

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 .

Subtract from .

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 .

Subtract from .

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 .

Multiply by .

Move to the left of .

Rewrite as .

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.

Add to 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 .

Add and .

Remove parentheses.

Simplify .

Subtract from .

Add and .

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 .

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.

Multiply by .

Multiply by .

Simplify by adding terms.

Subtract from .

Add and .

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.

Add to both sides of the equation.

Add and .

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 with in each equation.

Replace all occurrences of in with .

Replace all occurrences of in with .

Simplify.

Simplify .

Multiply by .

Subtract from .

Simplify .

Multiply by .

Subtract from .

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 .

Multiply by .

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 does not pass, since and . The function rule can’t be quadratic.

Since for the corresponding values, the function is not quadratic.

The function is not quadratic

The function is not quadratic

The function is not 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 .

Solve the equation for .

Rewrite the equation as .

Simplify each term.

Raise to the power of .

Move to the left of .

Raise to the power of .

Move to the left of .

Move to the left of .

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

Add to both sides of the equation.

Add to both sides of the equation.

Subtract from 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 .

Simplify each term.

Divide by .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

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.

Solve the equation for .

Rewrite the equation as .

Simplify .

Simplify each term.

Raise to the power of .

Move to the left of .

Raise to the power of .

Apply the distributive property.

Simplify.

Multiply by .

Multiply by .

Cancel the common factor of .

Factor out 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.

Move to the left of .

Move to the left of .

Simplify by adding terms.

Combine the opposite terms in .

Subtract from .

Add and .

Add and .

Add and .

Add and .

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 .

Divide by .

Solve the equation for .

Rewrite the equation as .

Simplify .

Simplify each term.

Raise to the power of .

Move to the left of .

Rewrite as .

Divide by .

Subtract from .

Raise to the power of .

Apply the distributive property.

Simplify.

Multiply by .

Multiply by .

Cancel the common factor of .

Move the leading negative in into the numerator.

Cancel the common factor.

Rewrite the expression.

Multiply by .

Simplify by adding terms.

Combine the opposite terms in .

Add and .

Add and .

Add and .

Add and .

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 .

Divide by .

Simplify .

Simplify each term.

Divide by .

Divide by .

Multiply by .

Simplify by adding and subtracting.

Subtract from .

Add and .

Reduce the system.

Simplify .

Multiply by .

Add and .

Remove parentheses.

Remove parentheses.

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 .

Multiply by .

Raise to the power of .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Simplify by adding zeros.

Add and .

Add and .

If the table has a cubic function rule, for the corresponding value, . This check does not pass, since and . The function rule can’t be cubic.

Since for the corresponding values, the function is not cubic.

The function is not cubic

The function is not cubic

The function is not cubic

There are no values for , , , and in the equations , , and that work for every pair of and .

The table does not have a function rule that is linear, quadratic, or cubic.

Find the Function Rule table[[x,y],[-3,221.86],[-2,37.71],[-1,6.41]]