How to draw the function x+5<7

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Discussion Overview

The discussion revolves around how to graph the inequality x + 5 < 7 and whether it can be considered a function. Participants explore the implications of the inequality and its representation on a Cartesian plane versus a number line.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether x + 5 < 7 qualifies as a valid function based on the definition of a function.
  • Another participant clarifies that the expression is an inequality, not a function.
  • It is noted that if the inequality involves only one variable, it should be graphed on a number line, while two-variable inequalities can be graphed on a Cartesian plane.
  • A participant describes how to graph the corresponding equation x + 5 = 7, stating it results in a vertical line at x = 2, with the solution set for the inequality being all points to the left of this line.
  • There is a reiteration of the previous point about graphing the inequality, emphasizing the vertical line at x = 2.
  • Another participant raises the question of whether graphing y = (x + 5) would yield different results, suggesting that it might not impose restrictions on the y-coordinate.
  • A later reply agrees that graphing y = (x + 5) would indeed yield different results, as the original inequality does not restrict the y-coordinate in the (x, y) coordinate pairs.

Areas of Agreement / Disagreement

Participants express differing views on whether the inequality can be considered a function and how to appropriately graph it. There is no consensus on the implications of graphing y = (x + 5) versus the inequality itself.

Contextual Notes

The discussion does not resolve the definitions and implications of functions versus inequalities, nor does it clarify the conditions under which each representation is valid.

Manula
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I am just interested in knowing, how to draw the function x+5<7 in a cartesian plane.
Since the definition of a function is, If For a certain input, there exist an out, then it is a function.
Is x+5<7 is a valid function then?
 
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What you wrote is an inequality, not a function.
 
If the inequality has only one variable (as yours does), you would graph the solution on a number line. If the inequality has two variables (x and y), then you could graph the solution on a Cartesian plane.
 
To draw a graph of this inequality, first draw the graph of the corresponding equation. x+ 5= 7. That. of course, is the same as "x= 2". It's graph, in a two dimensional "xy" graph, is the vertical line at x= 2. The set of points for which x+ 5< 7 is the set of points for which x< 2. That is, all points to the left of that vertical line.
 
HallsofIvy said:
To draw a graph of this inequality, first draw the graph of the corresponding equation. x+ 5= 7. That. of course, is the same as "x= 2". It's graph, in a two dimensional "xy" graph, is the vertical line at x= 2. The set of points for which x+ 5< 7 is the set of points for which x< 2. That is, all points to the left of that vertical line.

But if we take y=(x+5) and then, draw the graph, wouldn't it give different results??
 
Manula said:
But if we take y=(x+5) and then, draw the graph, wouldn't it give different results??

True.
Of the simple reason that the first inequality does not place any sort of restrictions on the y-coordinate in the points' (x,y) coordinate pairs.
 

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