# Algebra Examples

Find the Function Rule
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 .
Solve for in the first equation.
Replace all occurrences of in with
Replace all occurrences of in with
Replace all occurrences of in with
Replace all occurrences of in with
Solve for in the second equation.
Replace all occurrences of in with
Replace all occurrences of in with
Replace all occurrences of in with
Replace all occurrences of in with
Simplify.
Simplify .
Multiply by .
Add and .
Simplify .
Multiply by .
Add and .
Simplify .
Multiply by .
Add and .
Simplify .
Multiply by .
Add and .
Solve the third equation.
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 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 .
Solve for in the first equation.
Replace all occurrences of in with
Replace all occurrences of in with
Replace all occurrences of in with
Replace all occurrences of in with
Solve for in the second equation.
Replace all occurrences of in with
Replace all occurrences of in with
Replace all occurrences of in with
Replace all occurrences of in with
Solve for in the third equation.
Replace all occurrences of in with
Replace all occurrences of in with
Replace all occurrences of in with
Replace all occurrences of in with
Simplify.
Simplify .
Reduce the expression by cancelling the common factors.
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine the numerators over the common denominator.
Add and .
Divide by .
Simplify .
Reduce the expression by cancelling the common factors.
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine the numerators over the common denominator.
Subtract from .
Divide by .
Simplify .
Reduce the expression by cancelling the common factors.
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine the numerators over the common denominator.
Subtract from .
Divide by .
Simplify .
Simplify each term.
Reduce the expression by cancelling the common factors.
Cancel the common factor.
Divide by .
Multiply by .
Subtract from .
Solve the fourth equation.
Always true
Remove any equations from the system that are always true.
Solve the equation.
Always true
Remove any equations from the system that are always true.
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.
One to any power is one.
Multiply by .
Multiply by .
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 .
Calculate the value of such that when , , , and .
Simplify each term.
Raise to the power of .
Multiply by .
Multiply by .
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 .
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.
Add and .
Raise to the power of .
Multiply by .
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 .
Calculate the value of such that when , , , and .
Simplify each term.
Raise to the power of .
Multiply by .
Multiply by .
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 .
Calculate the value of such that when , , , and .
Simplify each term.
Raise to the power of .
Multiply by .
Multiply by .
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 .
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