Question

hi can someone help me with this problem where i need to find the range for the equation: y=(2/x+6)

Answer 1

let's us notice first that the domain, that is, the values "x" can take, must not make the denominator =0, so what values "x" MUST NOT take?

Answer 2

i mean -6

Answer 3

x cannot =-6 but how does that help with range, that only helps with finding the domain i think

Answer 4

so... yes... x cannont be -6, or it makes the denominator zero
other than that, "x" can take any positive vlaue or any negative value

so let's see what happens when say we give it a few values, let's see what happens to "y"

Answer 5

ok

Answer 6

gimme a sec

Answer 7

ok

Answer 8

hmm, one sec

Answer 9

ok

Answer 10

\(\large y = \cfrac{2}{x+6}\\ \quad \\ \quad \\

\begin{array}{llllllll}
x = 6&y = \cfrac{2}{x+6}& y = \cfrac{1}{6} \\
x = 5&y = \cfrac{2}{x+6}& y = \cfrac{2}{11}\\
x = 4&y = \cfrac{2}{x+6}& y = \cfrac{1}{5}\\
x = 3&y = \cfrac{2}{x+6}& y = \cfrac{2}{9}\\
x = 2&y = \cfrac{2}{x+6}& y = \cfrac{1}{4}\\
x = 1&y = \cfrac{2}{x+6}& y = \cfrac{2}{7}\\
x = 0&y = \cfrac{2}{x+6}& y = \cfrac{1}{3}\\
x = -1&y = \cfrac{2}{x+6}& y = \cfrac{2}{5}\\
x= -2&y = \cfrac{2}{x+6}& y = \cfrac{1}{2}\\
x = -3&y = \cfrac{2}{x+6}& y = \cfrac{2}{3}\\
x = -4&y = \cfrac{2}{x+6}& y = 1\\
x = -5&y = \cfrac{2}{x+6}& y = 2\\
x = -7&y = \cfrac{2}{x+6}& y = -2\\
x = -8&y = \cfrac{2}{x+6}& y = -1\\
x = -9&y = \cfrac{2}{x+6}& y = -\cfrac{2}{3}\\

\end{array}\)

Answer 11

okay so what does that mean

Answer 12

?

Answer 13

so notice how far up the range goes, at

x = -5 "y" is 2
x = -7 "y" goes down to -2


if it goes to the right of -5, is a fraction
if it goes to the left of -7, is a fraction too

a fraction is less than 1

Answer 14

range is the value of "y"

Answer 15

so.... what do you think would be the interval for the range, that is, for the value of "y"?

Answer 16

i have no idea?!

Answer 17

depending on values taken by "x", valid values, not like -6
"y" will take its value

the range is how far up and down "y" goes

Answer 18

i knew what range means but i dont get what would be the interval for range?

Answer 19

at x = -5 is how far UP it goes, +2
and at x = -7, is how far DOWN it goes -2

so the range would be [-2, 2]

Answer 20

okay i get it but isnt there a simpler way to do it i dont have to substitute all these values of x to find y right?

Answer 21

well, the other way would be graphing it

Answer 22

right i did that but i couldnt see the range on my calculator how do i find it on the calculator?

Answer 23

hmm... actually, the graphs shows ... a different range
http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiIyLyh4KzYpIiwiY29sb3IiOiIjMDAwMDAwIn0seyJ0eXBlIjoxMDAwLCJ3aW5kb3ciOlsiLTEyLjYyIiwiMC4zNzk5OTk5OTk5OTk5OTk0NSIsIi0xLjA0MDAwMDAwMDAwMDAwMDUiLCI2Ljk1OTk5OTk5OTk5OTk5OSJdfV0-

Answer 24

on that graph what would the range be?

Answer 25

the range is the values "y" takes, the vertical lines

Answer 26

right so would it be y is greater than or equal to 0, and y is less than or equal to 0?