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 |

Answered: Image /qna-images/answer/63064204-bac6-48fd-b594-57489c35543f.jpg

Answered: 1. f(x) = (x + 4)°(x + 1)²(x – 1)*…

Math

Algebra

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

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,...

See similar textbooks

Related questions

Q: Showthat the function f(x) = (3/x)+7 is decreasing for x denotes R - {0}

A: We have to show that function f(x) = (3/x) + 7 is decreasing for x € R - {0} We know that , f(x)…

Q: 5. Let f(x) = x² + 3x and g(x) = 2-x. (a) Find (f - g)(x) (b) Find (fg)(2) (c) Find (4) (x) and its…

Q: Find all relative extrema of f (æ) = 3x²/3 – 2æ %3D

A: Topic: differentiation

Q: f(x) = x* + x³ – 2x² For the above function state all intervals of x where f(x) is decreasing.

A: We know that if f'x>0 at a specific value of x, then the function f(x) is decreasing at those…

Q: Find the equation of the tan gent line to the graph of the equation f(x) = 5x - 8x +12, at the point…

A: Here we are going to solve only one question and for the remaining question post the question again.…

Q: Q1: - Find C that make the function f(x) continuous f(x) = {| x +3 Сх+ 6 x 2

Q: HW/ Graph (1) y= 1 x>1

Q: f(X) = 2/X g(X) = X+1/9 (What is the domain?)

Q: f(x) = (x – 3)^2 (3x – 1) Identify the maximum number of turning points.

A: The given function is f(x)=x-323x-1 We have to identify the maximum number of turning points.

Q: 2х + 14 if x – 3 2 if x = - 3

Q: 2) f(x)= 2x x2+1

A: Sol:- Extreme Points of 2xx2+1First Derivative Test definitionSuppose that x=c is a critical point…

Q: f(x) = x* + x³ – 2x² For the above function state all intervals of x where f(x) is positive.

A: solve the following

Q: Given f(x)= x^3 − 6x^2+9x, find the multiplicity of the zero at x = 3

Q: the function f(x) = k(x - s)(x - t)(x - u)^2 has: * O 3 zeros O 4 zeros O no turning points O 4…

A: Zeros of a function are those points where function has value zero. Hence f(x)=0 implies…

Q: Find removable discontinuities in f(x)=9x5-3x2+1

A: To remove discontinuity we need to factor numerator and denominator.

Q: 1 x-2 f(x)=- y g(x)=√x

A: To find the composite function

Q: Find the point of f(x) = 2x3 - 9x2-17x - 3 is at [0, 00) on which concavity changes. %3D

A: We draw graph of given function.

Q: state all intervals of x where f(x) is increasing.

A: TO FIND INTERVAL WHERE f(x) is INCREASING FIND f '(x) and see interval where f '(x) >0 f(x)…

Q: how can i find the difference quotient of g(x)= 11 over/ x+24

A: First of all, consider the formula for the difference quotient and the rational function g (x).

Q: 2) Find all relative extrema of ƒ(x)= x* – 4x³

A: Answer

Q: Consider the image attached of the graph of a function y = g(x) on the domain -8 <= x <= 8, which…

A: Label the points on the given graph as shown below.

Q: -kx + 1, x>4 a) Find the value k, if the function f (x) = (x² – 3x + 1, x 4

A: Given, fx = x2-3x+1, x≤4-kx+1, x >4 We have to find the value of k for which the…

Q: 32. For the function f(x) = 3X *5 Find: f (0) f(-2) f (3)

Q: 2. Let f(x) = -5x3/4 and g(x) = 7x3/4 Find (f+g)(x): evaluate at x = 81 %3D

A: Evaluation of the function at value x=81.

Q: f(x) = x(6 – x)-

A: Given :f(x)=xa(6-x)b 0≤x≤6

Question

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 |

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Inequality$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

please show fulll work and process
Graph the function f(x)=-sec(x/4)+3 on the interval [-2pi,6pi]
(42) For f(x) = -2x75 + 5x*° – 12x²5 + 10, the degree of f (x) is
For the function f(x) = 5/ x+2 4 2, find f-"(x). %3D Of (2) = (4 (x – 2)" Of (x) = (4x – 2) - Of(x) = 4x5 – 2 Of (x) = 4 (x – 2)° Submit Answer Privacy Policy Terms of Service Copyright © 2021 DeltaMath.com. All Rights Reserved.
f(x)=4X+2/(2x+1)(x-5) what is the point of discontinuation or hole has the coordinate as
Suppose point P (-2, -3) is on some function y=f(x) and is transformed to g(x) so that g(x) = 5f (-1/2 x + 3/2) + 4. Where does the point P get transformed to?