Graph a polynomial function of degree 3 or higher that has at least FOUR of the following criteria AND has at least one turning point AND goes through the point (6, -2) • Circle the letter that represents your chosen criteria in the chart below (you must have at least 4 circled) • Sketch as many zeros as needed, but use integers for the locations where the graph crosses the x-axis (don't use decimals for your zeros) Is symmetrical about the y-axis B. Ends in Quadrant 1 As x→∞0, y →∞ D. The function is decreasing on the interval 1 < x < 4 x18, y 18 Has f(-3) = 0 F. Has odd symmetry f(x) > 0 on the interval 5 < x < 8 H. Has end behaviour in the same direction Has an x-intercept with degree (order) three J. Has a local extrema (local maximum or minimum) when x = -2 that is not an absolute extrema Does not have an absolute maximum L. Has a range not equal to (-00,00)
Graph a polynomial function of degree 3 or higher that has at least FOUR of the following criteria AND has at least one turning point AND goes through the point (6, -2) • Circle the letter that represents your chosen criteria in the chart below (you must have at least 4 circled) • Sketch as many zeros as needed, but use integers for the locations where the graph crosses the x-axis (don't use decimals for your zeros) Is symmetrical about the y-axis B. Ends in Quadrant 1 As x→∞0, y →∞ D. The function is decreasing on the interval 1 < x < 4 x18, y 18 Has f(-3) = 0 F. Has odd symmetry f(x) > 0 on the interval 5 < x < 8 H. Has end behaviour in the same direction Has an x-intercept with degree (order) three J. Has a local extrema (local maximum or minimum) when x = -2 that is not an absolute extrema Does not have an absolute maximum L. Has a range not equal to (-00,00)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:a) Graph a polynomial function of degree 3 or higher that has at least FOUR of the following
criteria AND has at least one turning point AND goes through the point (6, -2)
Circle the letter that represents your chosen criteria in the chart below (you must have at
least 4 circled)
Sketch as many zeros as needed, but use integers for the locations where the graph crosses
the x-axis (don't use decimals for your zeros)
A
Is symmetrical about the y-axis
B.
Ends in Quadrant 1
C.
As x-00, y → ∞0
D.
The function is decreasing on the
interval 1 < x < 4
x → ∞0, y → -8
E.
Has f(-3) = 0
F.
Has odd symmetry
G.
f(x) > 0 on the interval 5 <x<8
H.
Has end behaviour in the same direction.
I. Has an x-intercept with degree (order) three
J.
Has a local extrema (local maximum or
minimum) when x = -2 that is not an
absolute extrema
K. Does not have an absolute maximum
L. Has a range not equal to (-00,00)
Your graph must also go through the point (6, -2)
b) Write the equation of your function, f(x) to represent the polynomial you graphed. Leave in
factored form. Show your work. The leading coefficient must be an exact value.
c) What is the minimum degree that your graphed function could be?
d) When is f(x) ≤ 0? (You can use your graph or a number line or a sign-analysis chart to
determine this answer. No work is required.)
Transcribed Image Text:e) If your function was divided by (x - 11), what would be the remainder?
f) Choose 2 of the given criteria in the chart that would have been impossible to use together in
the same graph. Explain why. (This does not connect to your graph, but is 2 criteria that
would be impossible to exists in the same graph together)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
