Question

graph each equation. identify the x and y-intercepts and the asymptotes of the graph.
y=1/x

Answer 1

@whpalmer4 help me again please.
sorry for bugging you

Answer 2

there is none

Answer 3

the graph of 1/x looks something like the crude diagram I've drawn:

Answer 4

To find the x-intercept, set \(y = 0\) and solve for \(x\). To find the y-intercept, set \(x = 0\) and solve for \(y\).

Answer 5

What do you think the asymptotes are?

Answer 6

well i have no clue what asymptotes are so i really dont know how to find them or anything

Answer 7

and when i go to see what they x and y intercepts are it says there is a error and will not tell me the answer. you cant divide 1/0 and 0*1 is 0 so your x =0 i dont get it
HELP :)

Answer 8

are you there??? @whpalmer4

Answer 9

help please

Answer 10

yes, I'm here :-)

Okay, the fact that you can't find a value that satisfies y = 1/0 or 0 = 1/x means that there are no such values.

Answer 11

in other words, the curve never intersects the x or y axes, so there are no x or y intercepts.

Answer 12

ok thats what i thought but i was also thinking maybe i was wrong :) ok so how do we find the asymptotes

Answer 13

The asymptotes are lines that the curve approaches arbitrarily closely, but never quite touches. Let's follow the curve out to the right. If \(x=1000000\), \(y = 1/1000000 = 0.000001\). If we go a million times as far to the right, \[x = 1000000000000, y = 0.000000000001\]And so on. Is there any positive value of \(x\) for which \(y\) is going to be a negative number?

Answer 14

i dont know im so lost

Answer 15

:/

Answer 16

@whpalmer4

Answer 17

Well, as x gets bigger and bigger, y gets smaller and smaller, but never reaches 0, much less becoming negative. That means that the curve on the right side of the y-axis never crosses the x-axis. It gets as close as imaginable, however. If you pick a distance to the x-axis, I can tell you the exact value of \(x\) that will make the curve be only that far away.

Does that suggest a possible (horizontal) asymptote to you?

Answer 18

umm maybe?? i not sure what a horizontal asymptote

Answer 19

A horizontal asymptote is an asymptote that is horizontal :-) In this case, the x-axis (y = 0) is a horizontal asymptote because the portion of \(y = 1/x\) gets arbitrarily close to it as \(x\) goes to \(+\infty\) but never quite gets there. On the left side of the graph, it's a horizontal asymptote because \(y = 1/x\) gets arbitrarily close to it (from below) as \(x\) goes to \(-\infty\) but again never quite gets there. Look at my drawing again with that in mind.

Answer 20

Does that make sense?

Answer 21

ok i have it graphed on my calculator. so the asymptotes a \[+\infty\] and \[-\infty \]

Answer 22

Similarly, for the vertical asymptote, the y-axis (x = 0) is going to be the vertical asymptote, as \(x\) approaches 0 but doesn't quite get there as \(y\) goes to \(+\infty\) or \(-\infty\).

Answer 23

so that is are asymptotes