Question

graph each equation. identify the x and y-intercepts and the asymptotes of the graph.
y=-1(over) x -4

Answer 1

@whpalmer4

Answer 2

Okay, you should be able to do this one. It's like the one I drew for you as "extra credit", except shifted by 2 more units along the x axis, and the flipped over (because it is -1/ instead of 1/)

Answer 3

it never hits the line again. so is when the denominator cant be 0 and x=2

Answer 4

Let me check something: the function is
\[y = \frac{-1}{x-4}\]Right? Not \[y = \frac{-1}{x} - 4\]

Answer 5

no it is the second one

Answer 6

Okay, glad I asked! That's a different transformation entirely!

Answer 7

ok good i was like that doesn't look like the one you gave me :)

Answer 8

Let's build this up piece by piece. Here's the graph of \(1/x\):

Answer 9

ok

Answer 10

continue

Answer 11

Now we have \(-1/x\), so wherever this one is positive, the other one is negative, and vice versa. In other words, we flip it over the \(x\) axis.

Answer 12

Looks like this:

Answer 13

ok i have the equation for the problem in the question graphed on my calculator

Answer 14

Now that was one part of the transformation. The next part is that we subtracted 4 from it. If we subtract 4 from the result of the function, that just moves the whole graph down by 4 units, right?

Answer 15

yes!!!

Answer 16

So that also moves the horizontal asymptote down by 4. Are we agreed that the asymptotes of \(1/x\) and \(-1/x\) are identical?

Answer 17

Please say "yes, of course!" :-)

Answer 18

i think they are. they are identical right?

Answer 19

ok i was right

Answer 20

Right. So one asymptote is going to stay the same, and one is going to change when we shift the whole graph down by 4 units. Can you tell me which is which?

Answer 21

so they asymptotes of -1/x is also x=0 and y=0 right

Answer 22

the graph will change the x=0 right?
they y=0 will stay the same

Answer 23

Yes, \(-1/x\) has asymptotes \(x = 0\) (vertical) and \(y = 0\) (horizontal)

Answer 24

ok is my other answer correct

Answer 25

Okay, I've updated my graph to include the line y = -4

Answer 26

no x=0 stays the same and the y will change!! Right????

Answer 27

yes, that's correct!

Answer 28

yes!!!!!! ok so will it change to y=4 or what??

Answer 29

also will the x and y intercepts still be 0

Answer 30

uh, here's my graph with the line y = 4 added...

Answer 31

oh its -4 sorry :/

Answer 32

remember, we had asymptotes of \(x = 0\) and \(y = 0\) before we shifted everything down by 4. when we shifted everything down by 4, the asymptotes also shifted, so the horizontal asymptote became \(y = -4\). The vertical asymptote is an infinitely long line, so we can't tell any different when it shifts :-)

Answer 33

Again, let's solve for the intercepts: put in \(x=0\) and solve for \(y\). Then put in \(y = 0\) and solve for \(x\).

Answer 34

You'll get one answer you've seen before, and one you haven't.

Answer 35

(that should have been "The vertical asymptote is an infinitely long line, so we can't tell any different when it shifts VERTICALLY")

Answer 36

ok so the asymptotes ar y=-4 and x=0 and the intercepts are y=0 and x=-5??

Answer 37

Wait a minute, how did you get those values for the intercepts?

\[y = -\frac{1}{x}-4\]\[y = -\frac{1}{0} -4 = \]

Answer 38

And \[0 = -\frac{1}x - 4\]\[4 = -\frac{1}{x}\]\[4x=-1\]\[x =\]

Answer 39

well when i plugged in 0 for x it said there was a error so i thought that y=0 oh and the x will be x=-1/4 or -.25

Answer 40

Yeah, if there's an error, there's no value. So the correct answers are
"no y-intercept" and "x = -1/4" and if you look at my graphs, you'll see the x-axis gets crossed at \(x=-1/4\) and the y-axis isn't crossed (because there's a vertical asymptote there).

Answer 41

ok so the intercepts are no y-intercept and x=-.25.
the asymptotes are x=0 and y=-4
correct?

Answer 42

yes! spoken like a true math geek :-)

Answer 43

though I'd go with x = -1/4 personally

Answer 44

lol ok thank you so much. i understand asymptotes now also. you are a lifesaver!!!! thank you again

Answer 45

it comes out exactly here, but not all fractions do. 1/3 = 0.333333333333...

Answer 46

not to rain on your parade, but you can also have asymptotes that aren't parallel to either x or y axis, and they are trickier to figure out :-) probably don't need to know about them yet, though!

Answer 47

at least I hope not, because I don't feel up to doing a good explanation of them :-)

Answer 48

i dont think so :D

Answer 49

well, if you need a refresher in a few days on this stuff, you know where to find me. I'm not always online, but I'll respond when I am.

Answer 50

ok thank you