Find The End Behavior F(x) - Mathway

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Algebra Examples Popular Problems Algebra Find the End Behavior f(x)=-(x-1)(x+2)(x+1)^2 Step 1Identify the degree of the function.Tap for more steps...Step 1.1Simplify and reorder the polynomial.Tap for more steps...Step 1.1.1Simplify by multiplying through.Tap for more steps...Step 1.1.1.1Apply the distributive property.Step 1.1.1.2Multiply by .Step 1.1.2Expand using the FOIL Method.Tap for more steps...Step 1.1.2.1Apply the distributive property.Step 1.1.2.2Apply the distributive property.Step 1.1.2.3Apply the distributive property.Step 1.1.3Simplify and combine like terms.Tap for more steps...Step 1.1.3.1Simplify each term.Tap for more steps...Step 1.1.3.1.1Multiply by by adding the exponents.Tap for more steps...Step 1.1.3.1.1.1Move .Step 1.1.3.1.1.2Multiply by .Step 1.1.3.1.2Multiply by .Step 1.1.3.1.3Multiply by .Step 1.1.3.1.4Multiply by .Step 1.1.3.2Add and .Step 1.1.4Rewrite as .Step 1.1.5Expand using the FOIL Method.Tap for more steps...Step 1.1.5.1Apply the distributive property.Step 1.1.5.2Apply the distributive property.Step 1.1.5.3Apply the distributive property.Step 1.1.6Simplify and combine like terms.Tap for more steps...Step 1.1.6.1Simplify each term.Tap for more steps...Step 1.1.6.1.1Multiply by .Step 1.1.6.1.2Multiply by .Step 1.1.6.1.3Multiply by .Step 1.1.6.1.4Multiply by .Step 1.1.6.2Add and .Step 1.1.7Expand by multiplying each term in the first expression by each term in the second expression.Step 1.1.8Simplify terms.Tap for more steps...Step 1.1.8.1Simplify each term.Tap for more steps...Step 1.1.8.1.1Multiply by by adding the exponents.Tap for more steps...Step 1.1.8.1.1.1Move .Step 1.1.8.1.1.2Use the power rule to combine exponents.Step 1.1.8.1.1.3Add and .Step 1.1.8.1.2Rewrite using the commutative property of multiplication.Step 1.1.8.1.3Multiply by by adding the exponents.Tap for more steps...Step 1.1.8.1.3.1Move .Step 1.1.8.1.3.2Multiply by .Tap for more steps...Step 1.1.8.1.3.2.1Raise to the power of .Step 1.1.8.1.3.2.2Use the power rule to combine exponents.Step 1.1.8.1.3.3Add and .Step 1.1.8.1.4Multiply by .Step 1.1.8.1.5Multiply by .Step 1.1.8.1.6Multiply by by adding the exponents.Tap for more steps...Step 1.1.8.1.6.1Move .Step 1.1.8.1.6.2Multiply by .Tap for more steps...Step 1.1.8.1.6.2.1Raise to the power of .Step 1.1.8.1.6.2.2Use the power rule to combine exponents.Step 1.1.8.1.6.3Add and .Step 1.1.8.1.7Rewrite using the commutative property of multiplication.Step 1.1.8.1.8Multiply by by adding the exponents.Tap for more steps...Step 1.1.8.1.8.1Move .Step 1.1.8.1.8.2Multiply by .Step 1.1.8.1.9Multiply by .Step 1.1.8.1.10Multiply by .Step 1.1.8.1.11Multiply by .Step 1.1.8.1.12Multiply by .Step 1.1.8.2Simplify by adding terms.Tap for more steps...Step 1.1.8.2.1Combine the opposite terms in .Tap for more steps...Step 1.1.8.2.1.1Add and .Step 1.1.8.2.1.2Add and .Step 1.1.8.2.2Subtract from .Step 1.1.8.2.3Add and .Step 1.2The largest exponent is the degree of the polynomial.Step 2Since the degree is even, the ends of the function will point in the same direction.EvenStep 3Identify the leading coefficient.Tap for more steps...Step 3.1Simplify the polynomial, then reorder it left to right starting with the highest degree term.Tap for more steps...Step 3.1.1Simplify by multiplying through.Tap for more steps...Step 3.1.1.1Apply the distributive property.Step 3.1.1.2Multiply by .Step 3.1.2Expand using the FOIL Method.Tap for more steps...Step 3.1.2.1Apply the distributive property.Step 3.1.2.2Apply the distributive property.Step 3.1.2.3Apply the distributive property.Step 3.1.3Simplify and combine like terms.Tap for more steps...Step 3.1.3.1Simplify each term.Tap for more steps...Step 3.1.3.1.1Multiply by by adding the exponents.Tap for more steps...Step 3.1.3.1.1.1Move .Step 3.1.3.1.1.2Multiply by .Step 3.1.3.1.2Multiply by .Step 3.1.3.1.3Multiply by .Step 3.1.3.1.4Multiply by .Step 3.1.3.2Add and .Step 3.1.4Rewrite as .Step 3.1.5Expand using the FOIL Method.Tap for more steps...Step 3.1.5.1Apply the distributive property.Step 3.1.5.2Apply the distributive property.Step 3.1.5.3Apply the distributive property.Step 3.1.6Simplify and combine like terms.Tap for more steps...Step 3.1.6.1Simplify each term.Tap for more steps...Step 3.1.6.1.1Multiply by .Step 3.1.6.1.2Multiply by .Step 3.1.6.1.3Multiply by .Step 3.1.6.1.4Multiply by .Step 3.1.6.2Add and .Step 3.1.7Expand by multiplying each term in the first expression by each term in the second expression.Step 3.1.8Simplify terms.Tap for more steps...Step 3.1.8.1Simplify each term.Tap for more steps...Step 3.1.8.1.1Multiply by by adding the exponents.Tap for more steps...Step 3.1.8.1.1.1Move .Step 3.1.8.1.1.2Use the power rule to combine exponents.Step 3.1.8.1.1.3Add and .Step 3.1.8.1.2Rewrite using the commutative property of multiplication.Step 3.1.8.1.3Multiply by by adding the exponents.Tap for more steps...Step 3.1.8.1.3.1Move .Step 3.1.8.1.3.2Multiply by .Tap for more steps...Step 3.1.8.1.3.2.1Raise to the power of .Step 3.1.8.1.3.2.2Use the power rule to combine exponents.Step 3.1.8.1.3.3Add and .Step 3.1.8.1.4Multiply by .Step 3.1.8.1.5Multiply by .Step 3.1.8.1.6Multiply by by adding the exponents.Tap for more steps...Step 3.1.8.1.6.1Move .Step 3.1.8.1.6.2Multiply by .Tap for more steps...Step 3.1.8.1.6.2.1Raise to the power of .Step 3.1.8.1.6.2.2Use the power rule to combine exponents.Step 3.1.8.1.6.3Add and .Step 3.1.8.1.7Rewrite using the commutative property of multiplication.Step 3.1.8.1.8Multiply by by adding the exponents.Tap for more steps...Step 3.1.8.1.8.1Move .Step 3.1.8.1.8.2Multiply by .Step 3.1.8.1.9Multiply by .Step 3.1.8.1.10Multiply by .Step 3.1.8.1.11Multiply by .Step 3.1.8.1.12Multiply by .Step 3.1.8.2Simplify by adding terms.Tap for more steps...Step 3.1.8.2.1Combine the opposite terms in .Tap for more steps...Step 3.1.8.2.1.1Add and .Step 3.1.8.2.1.2Add and .Step 3.1.8.2.2Subtract from .Step 3.1.8.2.3Add and .Step 3.2The leading term in a polynomial is the term with the highest degree.Step 3.3The leading coefficient in a polynomial is the coefficient of the leading term.Step 4Since the leading coefficient is negative, the graph falls to the right.NegativeStep 5Use the degree of the function, as well as the sign of the leading coefficient to determine the behavior.1. Even and Positive: Rises to the left and rises to the right.2. Even and Negative: Falls to the left and falls to the right.3. Odd and Positive: Falls to the left and rises to the right.4. Odd and Negative: Rises to the left and falls to the rightStep 6Determine the behavior.Falls to the left and falls to the rightStep 7

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