graphical representation of equation Y=1/x

Question

how to show graphically the representation of equation y= 1/x   (1divided by x)?

Answer 1

To follow up to Matt's answer with more detail there a just a couple things i'd like to note.

1) To get the Y value when X is a negative number simply continue the X-Y chart with negative inputs

 

x       y

2      1/2
3      1/3
4      1/4

 

-2    -1/2

-3    -1/3

...

-20   -1/20

 

You'll also note the similarity between the positive and negative inputs, that is [2 -> 1/2] and [-2 -> -1/2]. You can also see in the graph below this similarity results in the positive and negative lines being mirror images of each other (specifically over the x=-y line, which is a line passing through the origin (0,0) and at -45 degrees)

http://www4b.wolframalpha.com/Calculate/MSP/MSP51181ch2f4gi6hf404ih000053g9h1385g512661?MSPStoreType=image/gif&s=1&w=325.&h=151.&cdf=RangeControl

 

2) There is no x=0 or y=0 because when x=0 you end up dividing by zero which is impossible. The general rule to figure out what happens when you could end up dividing by zero on a graph is to get closer and closer to see what happens. In this case were getting closer and closer to x=0. I'll use positives because they are easier to work with but the same thing is happening with the negatives.

 

x                        y

1/10                  10

1/100                100

1/1000              1000

1/million           million 

1/billion            billion

and so on

 

You can see as the X input gets smaller and smaller, the Y result gets bigger and bigger; and this can continue on forever (as the denominator can increase forever). So as X gets closer to zero, Y gets closer to infinity (this will make sense once you've covered limits but the important idea to understand is the first sentence in this paragraph).

 

Obviously your graph can only go so high so you just draw the line going to the top of you graph, regardless of the scale. The first graph I posted went to y=4 while this one only goes to y=1

http://www4b.wolframalpha.com/Calculate/MSP/MSP51151ch2f4gi6hf404ih00001d415b8g44027cc3?MSPStoreType=image/gif&s=1&w=325.&h=148.&cdf=RangeControl

If you compare them they look the same just with different scales.

 

3) So while the positive side of the graph goes as high as possible, the negative side goes as low as possible. You don't have to worry about connecting the two sides because they don't connect. When you "divide by zero" weird things happen, in this case the answer is positive and negative infinity. So just like you don't divide by zero you don't graph x=0, and you don't connect the two sides of the graph across x=0.

Answer 2

when x gets very large (toward infinity) or very small (toward negative infinity), y gets very small and approaches the x-axis where y = o

 

when x gets near zero with small positive fractions, y gets very large toward infinity

when x gets near zero with small negative fractions, y gets very large toward negative infinity

 

x and y are either both positive or both negative

x and y are both never zero

 

So your graph is located in quadrants I and III

 

It does not touch or cross either the x-axis or y-axis

 

It looks like the letter L but with a curve in the corner instead of the sharp point in the first quadrant.

And it looks the same in the third quadrant but turned upside down.

 

It is symmetrical with respect to the origin.

 

The internet or a graphing calculator will also show you a picture.

Answer 3

to graph y = 1/x, first make a chart of values for x and y. For example

 

   x           y

 

  2          1/2

  3          1/3

  4          1/4

 

see how each "y" value is 1 over its corresponding "x" value?

 

Then draw a standard coordinate plane graph, with the x axis labeled as a number line from 0 to, say, 5. Then make its y axis go from 0 to 1/5, and plot points to represent the x,y pairs in your chart.

 

Done! :-)

 

hope this was helpful.

 

Matt