Review 7.1-7.2(Key) 1. Given graph: a. Number of turning points: b. Zeros: c. Even or odd degree function: Odd degree function; one end of the graph points up and the other end points down. d. Leading coefficient positive or negative: Positive; right-hand end of the graph points up. e. Equation of the function in factored form: 2. Given a. Find the degree (without multiplying through). The polynomial is equivalent to: The degree is the sum of the degrees of the factors. Add exponents: Degree is 6 b. Find the zeros and state the multiplicity for each. implies "how many times the zero occurs" Multiplicity 0 Multiplicity 1 Multiplicity 2 (notice exponent "2") Multiplicity 3 (notice exponent "3") Review: If zero has even multiplicity (example, 2, 4, 6, etc.), graph touches the but turns around x-axis If zero has odd multiplicity (example, 1, 3, 5, etc.), graph crosses the x-axis. 3. Determine if is a factor of . f is a factor of if and only if . is equivalent to , therefore, . If is a factor of the given polynomial function, then . Thus, is a factor of . Notice that, if we construct the graph of the given function we can see that the graph has a zero (x-intercept) at . 4. Use your calculator to find all the real zeros of the function 3. Approximate your answers to 4 decimal places.
Review 7.1-7.2(Key) 1. Given graph: a. Number of turning points: b. Zeros: c. Even or odd degree function: Odd degree function; one end of the graph points up and the other end points down. d. Leading coefficient positive or negative: Positive; right-hand end of the graph points up. e. Equation of the function in factored form: 2. Given a. Find the degree (without multiplying through). The polynomial is equivalent to: The degree is the sum of the degrees of the factors. Add exponents: Degree is 6 b. Find the zeros and state the multiplicity for each. Multiplicity implies "how many times the zero occurs" 0 Multiplicity 1 Multiplicity 2 (notice exponent "2") Multiplicity 3 (notice exponent "3") Review: If zero has even multiplicity (example, 2, 4, 6, etc.), graph touches the x-axis but turns around If zero has odd multiplicity (example, 1, 3, 5, etc.), graph crosses the x-axis. 3. Determine if is a factor of f . is a factor of if and only if . is equivalent to , therefore, . If is a factor of the given polynomial function, then . Thus, is a factor of . Notice that, if we construct the graph of the given function we can see that the graph has a zero (x-intercept) at . 4. Use your calculator to find all the real zeros of the function 3. Approximate your answers to 4 decimal places.
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