Using a graphing calculator to solve functions

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SUMMARY

The discussion focuses on using a graphing calculator to analyze the function f(x) = x^7 - 4x^5 - 3x^4 + 4x^3 + 12x^2 - 12/x^7. Participants are tasked with graphing the function over specified intervals to estimate x-intercepts. Key insights include the importance of adjusting viewing windows for accurate graph representation and the necessity of careful estimation techniques when identifying x-intercepts. The conversation emphasizes practical strategies for effectively utilizing graphing calculators in function analysis.

PREREQUISITES
  • Understanding of polynomial functions and their properties
  • Familiarity with graphing calculators, specifically model features
  • Knowledge of adjusting viewing windows for graphing
  • Basic skills in estimating x-intercepts from graphs
NEXT STEPS
  • Learn how to adjust viewing windows on specific graphing calculator models
  • Explore techniques for estimating x-intercepts from polynomial graphs
  • Study the behavior of higher-degree polynomial functions
  • Investigate the use of graphing calculators for complex function analysis
USEFUL FOR

Students, educators, and anyone using graphing calculators for mathematical analysis, particularly those working with polynomial functions and seeking to improve their graphing skills.

arl2267
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Consider the function:

f(x)= x7-4x5-3x4+4x3+12x2-12/x7

a) Graph the function on [-6,6] by [-6,6]. From your graph, estimate how many x-intercepts the function has and what values they are.

b) Now graph the function on [-1.5, -1.4] by [-10-4, 10-4] and on [1.4, 1.5] by [-10-5, 10-5] From your graphs, estimate how many x-intercepts the function has and what their values are.

c)From your results in part a and b what advice would you give a friend using a graphing calculator to find x-intercepts?

I'm not even sure where to start with this problem. Just looking at part b gives me a headache and I have no idea what I'm doing. Any help would be greatly appreciated. Thanks.
 
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What model calculator do you have? Do you know how to adjust viewing windows on your model?
 

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