Algebra Examples

Find the Function Rule
Check if the function rule is linear.
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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 .
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Solve for in the first equation.
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Solve for in the second equation.
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Simplify.
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Simplify the right side.
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Multiply by to get .
Add and to get .
Simplify the right side.
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Multiply by to get .
Add and to get .
Simplify the right side.
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Multiply by to get .
Add and to get .
Solve for in the third equation.
No solution
Solve for in the fourth equation.
No solution
No solution
No solution
No solution
Calculate the value of such that when , , and .
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Simplify each term.
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Multiply by to get .
Multiply by to get .
Add and to get .
If the table has a linear function rule, for the corresponding value, . This check passes since and .
Calculate the value of such that when , , and .
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Simplify each term.
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Multiply by to get .
Multiply by to get .
Add and to get .
If the table has a linear function rule, for the corresponding value, . This check passes since and .
Calculate the value of such that when , , and .
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Simplify each term.
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Multiply by to get .
Multiply by to get .
Add and to get .
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
Check if the function rule is quadratic.
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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 .
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Solve for in the first equation.
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Solve for in the second equation.
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Solve for in the third equation.
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Simplify.
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Divide by to get .
Simplify the right side.
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Simplify each term.
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Multiply by to get .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Divide by to get .
Multiply by to get .
Add and to get .
Simplify the right side.
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Multiply by to get .
Add and to get .
Solve for in the fourth 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.
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Calculate the value of such that when , , , and .
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Simplify each term.
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Multiply by to get .
Remove parentheses around .
One to any power is one.
Multiply by to get .
Multiply by to get .
Simplify by adding numbers.
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Add and to get .
Add and to get .
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 .
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Simplify each term.
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Multiply by to get .
Remove parentheses around .
Raise to the power of to get .
Multiply by to get .
Multiply by to get .
Simplify by adding numbers.
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Add and to get .
Add and to get .
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 .
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Simplify each term.
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Multiply by to get .
Remove parentheses around .
Raise to the power of to get .
Multiply by to get .
Multiply by to get .
Simplify by adding numbers.
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Add and to get .
Add and to get .
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 .
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Simplify each term.
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Multiply by to get .
Remove parentheses around .
Raise to the power of to get .
Multiply by to get .
Multiply by to get .
Simplify by adding numbers.
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Add and to get .
Add and to get .
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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