How Do You Draw a Function from Its Equation?

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SUMMARY

The discussion focuses on the process of graphing the function y = x + 1, emphasizing its slope of 1 and y-intercept of 1. Participants clarify that understanding how to plot straight lines and parabolas is essential for accurately representing the function. The conversation highlights the importance of recognizing the behavior of the graph in different regions, particularly for x < -1. Overall, the exchange provides a clear method for visualizing linear functions based on their equations.

PREREQUISITES
  • Understanding of linear equations and their graphical representations
  • Familiarity with the concepts of slope and y-intercept
  • Basic skills in plotting functions on a Cartesian plane
  • Knowledge of piecewise functions for analyzing different segments of graphs
NEXT STEPS
  • Learn how to graph quadratic functions, specifically parabolas
  • Study the concept of slope-intercept form in greater detail
  • Explore the use of graphing calculators or software for function visualization
  • Investigate piecewise functions and their applications in real-world scenarios
USEFUL FOR

Students learning algebra, educators teaching graphing techniques, and anyone interested in mastering the visualization of mathematical functions.

PhanicKnight
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Homework Statement


I need to draw this function:
upload_2016-12-8_18-49-49.png

however I don't get how?
I have the solution
upload_2016-12-8_18-51-36.png

but I don't understand how do I get that from the given function. Someone please try to explain? Thanks
 
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PhanicKnight said:

Homework Statement


I need to draw this function:
View attachment 110120
however I don't get how?
I have the solution
View attachment 110121
but I don't understand how do I get that from the given function. Someone please try to explain? Thanks

Can you plot straight lines and parabolas? If so, plot the graph of ##y=x+1##. It has slope ##1## and ##y## intercept ##1##. Notice that the part of your graph where ##x < -1## agrees with your graph, so just keep that part. Similarly, do the other two parts.
 
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Yes, that does it. I feel too dumb right now. Ah, thank you.
 

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