Graphing inequality with mod function

In summary, to graph the inequality -|y| + 1/2 >= e-|x|, you can draw the function for equality which would be symmetric in all quadrants and intersect the axes at +ln2 and -ln2 (x-axis) and 1/2 and -1/2 (y-axis). The inequality can then be rewritten as y >= e-|x| - 1/2 or y <= -e-|x| + 1/2.
  • #1
aim1732
430
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How can we graph this inequality - |y|+1/2>=e-|x| ?
I drew the function(actually a combination of functions) for equality. It would be symmetric in all quadrants and intersect the axes at +ln2 and -ln2(x-axis) and 1/2 and -1/2(y-axis).However since the various graphs are mixed up it is hard pinpoint what region to take.

I have attached one half of the actual graph.
The other half is it's reflection on the x-axis.
 

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  • #2
aim1732 said:
How can we graph this inequality - |y|+1/2>=e-|x| ?
I drew the function(actually a combination of functions) for equality. It would be symmetric in all quadrants and intersect the axes at +ln2 and -ln2(x-axis) and 1/2 and -1/2(y-axis).However since the various graphs are mixed up it is hard pinpoint what region to take.

I have attached one half of the actual graph.
The other half is it's reflection on the x-axis.
Your inequality is equivalent to |y| >= e-|x| - 1/2. This can be rewritten as
y >= e-|x| - 1/2 or -y >= e-|x| - 1/2

So y >= e-|x| - 1/2 or y <= -e-|x| + 1/2

Does that help?
 
  • #3
Yes I should have considered the intervals for the different inequalities.Thanks a lot.
 

FAQ: Graphing inequality with mod function

1. What is a mod function in graphing inequality?

A mod function, short for modulus function, is a mathematical function that calculates the remainder after dividing a number by another number. This function is often used in graphing inequalities to represent absolute value.

2. How do you graph an inequality with a mod function?

To graph an inequality with a mod function, you first need to rewrite the inequality using the modulus symbol (|). Then, plot the resulting equation on a number line, with the midpoint at 0. Finally, shade the area to the right or left of the midpoint, depending on whether the inequality is greater than or less than.

3. What does the absolute value symbol mean in a mod function graph?

The absolute value symbol (|) in a mod function graph represents the distance of a number from zero on a number line. This symbol is used to indicate the magnitude of a number without regard to its sign.

4. Can you graph a mod function inequality on a coordinate plane?

Yes, a mod function inequality can be graphed on a coordinate plane. To do so, you would need to first rewrite the inequality in terms of x and y, and then plot the resulting equation on the coordinate plane. The graph will represent the solutions to the inequality in the form of a shaded region.

5. How do you determine the solution to a mod function inequality?

To determine the solution to a mod function inequality, you would need to look at the shaded region on the graph and identify the values that satisfy the inequality. These values will be shown on the number line or coordinate plane, depending on the type of graph used.

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