Question

How to graph this simple equation?

Answer 1

\[y=\frac{ 1 }{ 1+x ^{2} }\]

Answer 2

so when x gets big, what happens to the fraction?

Answer 3

the value gets switched/upside down? I have no clue at all.

Answer 4

just plug some numbers in, I recommend 10, 100, 10000, etc

Answer 5

what value does the fraction seem to approach

Answer 6

the value shrinks?

Answer 7

yes, it gets smaller and smaller, and close to what number?

Answer 8

to nearly 0?

Answer 9

right, so we call that the limit as x goes to infinity =0

Answer 10

just an fyi. Now, we want to see what the biggest that fraction can equal

Answer 11

so, any guesses?

Answer 12

No, can't come up with any.

Answer 13

no attempt? Please try.

Answer 14

What you mean what the biggest fraction that can equal? 1=1 or something like that?

Answer 15

I get this for the graph

Answer 16

LOL

Answer 17

yea, the biggest the fraction can be is one. can't be anything more than 1/1

Answer 18

cross the y-axis at 1.0

Answer 19

so when does the fraction equal one?

Answer 20

0

Answer 21

good, so now, you have some points to the right, of zero x=1,10,100 etc, we plot those, then since we know it is gonna get close to 0 after maybe x=5, we just make our graph line really really close to zero but never equaling zero. So, we need values to the left of zero now

Answer 22

any thoughts on what it will look like?

Answer 23

Since, it crosses the y-axis at (1,0), that would be the line of symmetry. X values would be -0.5, -1 for the left and 0.5, 1 for the right?

Answer 24

it does not cross the y axis at (1,0)

Answer 25

and no, you can only attain 1 once

Answer 26

so to graph it, X values for -5, -10, 5, 10?

Answer 27

why are you doing multiples of 5?

Answer 28

you should have already graphed the right half

Answer 29

I thought any numbers would be fine as long the value is close to 0, but not equal 0?

Answer 30

they are, but no need to make it harder on yourself

Answer 31

you really only need maybe 5 points total to get the gist of the graph

Answer 32

x=0 must be a point graphed

Answer 33

now, pick 4 more easy points, 2 to the left and 2 to the right of zero. Connect the dots in a curvy fashion, and you are done