The image presents a multiple-choice question regarding polynomial functions:**Question:**Which of the following is a polynomial function that might have the given graph?**Options:**- **A.** \( f(x) = 2x(x + 3)^2(x - 3)^2 \)- **B.** \( f(x) = -2x(x - 3)^2(x - 3)^2 \)- **C.** \( f(x) = 2x(x + 3)(x - 3) \)- **D.** \( f(x) = -2x(x + 3)^2(x + 3)^2 \)- **E.** \( f(x) = -2x(x + 3)^2(x - 3)^2 \)- **F.** \( f(x) = -2x(x + 3)(x - 3) \)Note: The graph that corresponds to these polynomial functions is not shown in the image. **Problem Statement:**Write a polynomial function whose graph is shown below (use the smallest degree possible). The coordinates of the indicated point are \((-2, 100)\).**Graph Explanation:**The graph depicts a polynomial curve plotted on a Cartesian plane with both x and y axes labeled and equally spaced. The x-axis ranges from -5 to 5, while the y-axis spans from -150 to 150.Key Features of the Graph:- The curve crosses the y-axis upward at approximately 20.- There are turning points indicating local maximums and minimums; the curve has a local maximum at around \(x = -1.5, y = 90\) and a local minimum around \(x = 2.5, y = -120\).- There is an indicated specific point on the graph at \((-2, 100)\).- The curve represents fluctuations typical of a polynomial of degree at least 3, as observed from the number of turning points.The task is to determine a polynomial equation that fits this graph, taking into account its characteristics and the coordinates provided.

Which of the following is a polynomial function that might have the given graph? O A. f(x) = 2x(x+ 3)2 (x - 3)2 O B. f(x) = - 2x(x- 3)2(x-3)2 O C. f(x) = 2x(x+3)(x-3) O D. f(x) = - 2x(x+3)2 (x+ 3)2 O E. f(x) = - 2x(x+3)2(x-3)2 O F. f(x) = - 2x(x+3)(x- 3)

Which of the following is a polynomial function that might have the given graph? O A. f(x) = 2x(x+ 3)2 (x - 3)2 O B. f(x) = - 2x(x- 3)2(x-3)2 O C. f(x) = 2x(x+3)(x-3) O D. f(x) = - 2x(x+3)2 (x+ 3)2 O E. f(x) = - 2x(x+3)2(x-3)2 O F. f(x) = - 2x(x+3)(x- 3)

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Q: 2. Which of the following is an example of a polynomial function? -cif a. f(x) =+3x – 1 C. f(x) =…

Q: The function given by f(x) = -3x + V2x + -x (is/is not) a polynomial function.

A: A polynomial is a function such as quadratic, cubic and so on which involve only non-negative…

Q: Select from the following which is the polynomial function that has the given zeros. 0, - 7, -3 O…

Q: If f is a polynomial function, and x − 6 is a factor of f ( x ), what is the value of f ( 6 ) ?

A: Answer is 0 Explanation is given below..

Q: Which of the following is NOT a polynomial function? O A. f(x) = 0 O B. f(x) = 1 O C. f(x) = x2 + x…

A: Let's find.

Q: If f is a polynomial function and x-4 is a factor of f, then f (4) .

A: A polynomial function is a function that involves only positive powers in equation . The general…

Q: Which is the graph of the polynomial function p(x) = (x-1)(x+1)(x-4)? 241r 24fr y p(x) 16 16 8 8- -6…

Q: what is the degree of the polynomial function y = x(x-1)3(x+1)2

A: So the polynomial is y=x(x-1)3(x+1)2 On simplfying y= x(x3-1-3x2+3x)(x2+2x+1) Adding the Highest…

Q: 10. Sketch the graph of each polynomial function. Make sure you show all intercepts and proper end…

A: Explanation of the answer is as follows

Q: Which of the following polynomial functions has a graph that crosses the x- axis at (-4,0)? A. f(x)…

A: Let's find.

Q: Graph the polynomial function using a calculator. f(x) = x(x – 4)(x + 4) y 6아 60 4아 4아 2아 2아 -8 -6…

Q: Find the graph of the polynomial function P(x) = x² + 2. -20 -16 -3 -12 -8 M 4 3 N -1 2 دی T in 20…

Q: 8. Find one zero of the polynomial f(x)=2x-x-6x+3 %3D

A: Given function is: Apply rational root theorem to get roots of polynomial. If the polynomial has a…

Q: Simplify each polynomial function. Be very careful! -10(u + v) + 8(u - 1) - 3(u + 6) = 7x -[2(x² -…

Q: 12. Which polynomial function has its end behavior extending from quadrants 1 to 2? a. f(x) = x³ – 9…

A: y=f(x), in 1st quadrant x and y are both positive In 2nd quadrant x is negative and y is positive…

Q: Write an equation for the polynomial function graphed below 6 + 5 4 + + -5 -4 -B -2 y(x) = 3 2 1 -1…

A: Concept to be used: Let us consider a polynomial of degree p has zeroes at x=x1,x2,x3, . . . ,xn.…

Q: For the polynomial function y = (x + 4)2 (x + 1)(x – 3)3 find the following List the factors, zeros…

Q: Graph the following polynomial functions. Label the x- and y- intercept(s) each) on the graph. (4…

Q: Select all correct answers.

A: A polynomial graph must be smooth, continuous and does not have sharp turning points. also the…

Question

**Problem Statement:**

Write a polynomial function whose graph is shown below (use the smallest degree possible). The coordinates of the indicated point are \((-2, 100)\).

**Graph Explanation:**

The graph depicts a polynomial curve plotted on a Cartesian plane with both x and y axes labeled and equally spaced. The x-axis ranges from -5 to 5, while the y-axis spans from -150 to 150.

Key Features of the Graph:
- The curve crosses the y-axis upward at approximately 20.
- There are turning points indicating local maximums and minimums; the curve has a local maximum at around \(x = -1.5, y = 90\) and a local minimum around \(x = 2.5, y = -120\).
- There is an indicated specific point on the graph at \((-2, 100)\).
- The curve represents fluctuations typical of a polynomial of degree at least 3, as observed from the number of turning points.

The task is to determine a polynomial equation that fits this graph, taking into account its characteristics and the coordinates provided.

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Does the following photo show the graph of a polynomial function?
t Write an equation for the polynomial graphed below + -5 -4 + int y(x) = -2 6 + 5- 4+ 3 + 2+ 1- + -2 + -3+ -4 -5 -6 + + 2 3 4 Lin 5 a
ACT 5

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning