Complete a table and graph a linear function calculator

Our online expert tutors can answer this problem

Get step-by-step solutions from expert tutors as fast as 15-30 minutes. Your first 5 questions are on us!

Number Line

Step 1

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 .

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 .

Apply the distributive property.

Replace all occurrences of in with .

Apply the distributive property.

Replace all occurrences of in with .

Apply the distributive property.

Replace all occurrences of in with .

Apply the distributive property.

Rewrite the equation as .

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

Add to both sides of the equation.

Divide each term in by and simplify.

Cancel the common factor of .

Cancel the common factor.

Replace all occurrences of with in each 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 .

Since is not true, there is no solution.

No solution

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

The function is not linear

The function is not linear

Step 2

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 .

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 .

Apply the distributive property.

Simplify by adding terms.

Replace all occurrences of in with .

Apply the distributive property.

Simplify by adding terms.

Replace all occurrences of in with .

Apply the distributive property.

Simplify by adding terms.

Replace all occurrences of in with .

Apply the distributive property.

Simplify by adding terms.

Rewrite the equation as .

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.

Divide each term in by and simplify.

Cancel the common factor of .

Cancel the common factor.

Cancel the common factor of and .

Cancel the common factors.

Cancel the common factor.

Move the negative in front of the fraction.

Replace all occurrences of with in each equation.

Replace all occurrences of in with .

Apply the distributive property.

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

Combine the numerators over the common denominator.

Replace all occurrences of in with .

Apply the distributive property.

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

Combine the numerators over the common denominator.

Move the negative in front of the fraction.

Replace all occurrences of in with .

Apply the distributive property.

Cancel the common factor of .

Move the leading negative in into the numerator.

Cancel the common factor.

Simplify by adding terms.

Replace all occurrences of in with .

Apply the distributive property.

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

Combine the numerators over the common denominator.

Rewrite the equation as .

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

Subtract from both sides of the equation.

Divide each term in by and simplify.

Cancel the common factor of .

Cancel the common factor.

Replace all occurrences of with in each 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 .

Cancel the common factor of and .

Cancel the common factors.

Cancel the common factor.

Remove any equations from the system that are always true.

List all of the solutions.

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 by adding and subtracting.

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 by adding and subtracting.

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 .

Multiply by by adding the exponents.

Use the power rule to combine exponents.

Simplify by adding and subtracting.

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 by adding and subtracting.

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 by adding and subtracting.

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

Step 3

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

How do you determine a linear function from a table and graph?