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1. f(x) = (x + 4)°(x + 1)²(x – 1)* Zeros Multiplicity Crosses/Touches Degree Sign End behavior

1. f(x) = (x + 4)°(x + 1)²(x – 1)* Zeros Multiplicity Crosses/Touches Degree Sign End behavior

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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For the following polynomial functions: a. **State the degree and the sign of the leading coefficient.** Write out the words positive and negative! Then use the information to determine the end behavior of the graph using the arrow notation as discussed in class (see the example below). b. **List all of the real zeros with their multiplicity and state the behavior of each zero at the x-axis,** i.e. crosses or touches. Write out the words crosses and touches! c. **Based on parts (a) and (b), draw a rough sketch of the graph without using a calculator.** --- **Example:** \( p(x) = 3(x + 4)^3(x + 1)(x - 5)^2 \) | Zeros | Multiplicity | Crosses/Touches | |-------|--------------|-----------------| | -4 | 3 | Crosses | | 1 | 1 | Crosses | | 5 | 2 | Touches | - **Degree:** 6 - **Sign:** Positive - **End Behavior:** \( \uparrow \quad \uparrow \) The example graph is shown with arrows pointing upwards on both ends, indicating the end behavior as \( \uparrow \quad \uparrow \). --- **Problems:** 1. **\( f(x) = (x + 4)^3(x + 1)^2(x - 1)^4 \)** | Zeros | Multiplicity | Crosses/Touches | |-------|--------------|-----------------| | | | | - **Degree:** - **Sign:** - **End Behavior:** (Graph sketch with appropriate arrows showing end behavior) 2. **\( h(x) = -7(x + 2)^2(x - 4)^2 \)** | Zeros | Multiplicity | Crosses/Touches | |-------|--------------|-----------------| | | | | - **Degree:** - **Sign:** - **End Behavior:** (Graph sketch with appropriate arrows showing end behavior) 3. **\( j(x) = 8(x + 3)(x + 1)^2(x - 2)^3(x - 5)^4 \)** | Zeros | Multiplicity | Crosses/Touches |
Transcribed Image Text:For the following polynomial functions: a. **State the degree and the sign of the leading coefficient.** Write out the words positive and negative! Then use the information to determine the end behavior of the graph using the arrow notation as discussed in class (see the example below). b. **List all of the real zeros with their multiplicity and state the behavior of each zero at the x-axis,** i.e. crosses or touches. Write out the words crosses and touches! c. **Based on parts (a) and (b), draw a rough sketch of the graph without using a calculator.** --- **Example:** \( p(x) = 3(x + 4)^3(x + 1)(x - 5)^2 \) | Zeros | Multiplicity | Crosses/Touches | |-------|--------------|-----------------| | -4 | 3 | Crosses | | 1 | 1 | Crosses | | 5 | 2 | Touches | - **Degree:** 6 - **Sign:** Positive - **End Behavior:** \( \uparrow \quad \uparrow \) The example graph is shown with arrows pointing upwards on both ends, indicating the end behavior as \( \uparrow \quad \uparrow \). --- **Problems:** 1. **\( f(x) = (x + 4)^3(x + 1)^2(x - 1)^4 \)** | Zeros | Multiplicity | Crosses/Touches | |-------|--------------|-----------------| | | | | - **Degree:** - **Sign:** - **End Behavior:** (Graph sketch with appropriate arrows showing end behavior) 2. **\( h(x) = -7(x + 2)^2(x - 4)^2 \)** | Zeros | Multiplicity | Crosses/Touches | |-------|--------------|-----------------| | | | | - **Degree:** - **Sign:** - **End Behavior:** (Graph sketch with appropriate arrows showing end behavior) 3. **\( j(x) = 8(x + 3)(x + 1)^2(x - 2)^3(x - 5)^4 \)** | Zeros | Multiplicity | Crosses/Touches |
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