Graphs and Complex Number: (1 Viewer)

[umm what]

Can someone answer the questions in the attachment?

THANKS

 

[SpiralFlex]

We need to powerful method of discussion here.

For the first one we have some sort of weird looking graph.



Now, from the graph you could notice a few things. One obvious thing is:

- As the function tends toward positive and negative infinity, it approaches the asymptote of -1.

This of course only can happen if g(x) takes a negative value AND if it holds the same degree as that of the denominator.

With this in mind the only possible answer is D.

[HR][/HR]

Now let's consider the second one.

A) Well it's quite obvious that Q(w) is P(z) rotated anti-clockwise 90 degrees and halved in length. So of course A is correct.

B) Is incorrect. It is saying that the vector is rotated 90 degrees clockwise then truncated by half its length. Not true.

C) If we were to take the conjugate of w, it would be a reflect about the x axis. Clearly it cannot be rotated 90 degrees in any way to form the vector of z.

D)





Same as first one! CORRECT!

[HR][/HR]

Next question.

Consider A, a is correct, because the conjugate is the reflection about the x axis. You may be thinking if might be some angle say 11pi/6 rads. However we are concerning the principle values. So adding them will result in zero. Hence A is correct.

Consider B, Clearly, the angle made with the positive real axis minus the argument made by z is 90! Correct!

Consider C, NOPE! By observation!

Consider D, Correct. If we put some hypothetical values in, we always get -90!

[HR][/HR]

Next one. If we take the reciprocal function, it will always retain it's y value of 1 at the x coordinate. So the only possible answer is A.


Help me get off this website. It's ruining my HSC!

 

[umm what]

for the last question, isnt it B) ??

We need to powerful method of discussion here.

For the first one we have some sort of weird looking graph.



Now, from the graph you could notice a few things. One obvious thing is:

- As the function tends toward positive and negative infinity, it approaches the asymptote of -1.

This of course only can happen if g(x) takes a negative value AND if it holds the same degree as that of the denominator.

With this in mind the only possible answer is D.

[HR][/HR]

Now let's consider the second one.

A) Well it's quite obvious that Q(w) is P(z) rotated anti-clockwise 90 degrees and halved in length. So of course A is correct.

B) Is incorrect. It is saying that the vector is rotated 90 degrees clockwise then truncated by half its length. Not true.

C) If we were to take the conjugate of w, it would be a reflect about the x axis. Clearly it cannot be rotated 90 degrees in any way to form the vector of z.

D)





Same as first one! CORRECT!

[HR][/HR]

Next question.

Consider A, a is correct, because the conjugate is the reflection about the x axis. You may be thinking if might be some angle say 11pi/6 rads. However we are concerning the principle values. So adding them will result in zero. Hence A is correct.

Consider B, Clearly, the angle made with the positive real axis minus the argument made by z is 90! Correct!

Consider C, NOPE! By observation!

Consider D, Correct. If we put some hypothetical values in, we always get -90!

[HR][/HR]

Next one. If we take the reciprocal function, it will always retain it's y value of 1 at the x coordinate. So the only possible answer is A.


Help me get off this website. It's ruining my HSC!

 

[umm what]

the horizontal asymtote remains at 1 coz reciprocal of 1 is 1 ...

We need to powerful method of discussion here.

For the first one we have some sort of weird looking graph.



Now, from the graph you could notice a few things. One obvious thing is:

- As the function tends toward positive and negative infinity, it approaches the asymptote of -1.

This of course only can happen if g(x) takes a negative value AND if it holds the same degree as that of the denominator.

With this in mind the only possible answer is D.

[HR][/HR]

Now let's consider the second one.

A) Well it's quite obvious that Q(w) is P(z) rotated anti-clockwise 90 degrees and halved in length. So of course A is correct.

B) Is incorrect. It is saying that the vector is rotated 90 degrees clockwise then truncated by half its length. Not true.

C) If we were to take the conjugate of w, it would be a reflect about the x axis. Clearly it cannot be rotated 90 degrees in any way to form the vector of z.

D)





Same as first one! CORRECT!

[HR][/HR]

Next question.

Consider A, a is correct, because the conjugate is the reflection about the x axis. You may be thinking if might be some angle say 11pi/6 rads. However we are concerning the principle values. So adding them will result in zero. Hence A is correct.

Consider B, Clearly, the angle made with the positive real axis minus the argument made by z is 90! Correct!

Consider C, NOPE! By observation!

Consider D, Correct. If we put some hypothetical values in, we always get -90!

[HR][/HR]

Next one. If we take the reciprocal function, it will always retain it's y value of 1 at the x coordinate. So the only possible answer is A.


Help me get off this website. It's ruining my HSC!

 

[SpiralFlex]

No? There is no horizontal asymptote for the original graph. It just indicates the line y=1

 

[umm what]

ok but how do u know its A) ??

No? There is no horizontal asymptote for the original graph. It just indicates the line y=1

 

[SpiralFlex]

Which one? I need to go now. List questions and I will get back to you ASAP tonight. If not, PM me.

 

[umm what]

how does the line y=1 moves down by a 1/2 ??

No? There is no horizontal asymptote for the original graph. It just indicates the line y=1

 

[SpiralFlex]

I never claimed that, although it is true.

All I simply said was, when you reciprocate the coordinates, you get the same y oordinate with the x coordinate. Hence the only possible answer is B.

 

[umm what]

u said its A) first ... thanks anyway

I never claimed that, although it is true.

All I simply said was, when you reciprocate the coordinates, you get the same y oordinate with the x coordinate. Hence the only possible answer is B.

 

[SpiralFlex]

Sorry its A. I got the first and last question mixed up.

 

[umm what]

wait is it A) for last question?? the graph question????

Sorry its A. I got the first and last question mixed up.

 

[EazyEEE]

last questions for the reciprol graph is a, because u eliminate d since f(x) and 1/f(x) must have same signs, and for f(x) =1, 1/f(x) must also equals to 1,

so its common sense

 

[Aesytic]

the answer to the graphs question is A
i assume you know why it can't be C or D
with B, the graph suggests that 1/f(x) approaches 1 as x approaches infinity. if we look at the original graph, in order for this to be true, f(x) would also need to have a horizontal asymptote at 1. however, this isn't the case. the graph clearly shows that the curve doesn't approach 1 (the line y=1 is shown just to indicate that at x=1 and -1, f(x) = 1 as well)
hence the answer can only be A. as to why the line moves from 1 down to a half, it is to show the turning point of the middle part of the curve (the "parabola") since there was a maximum at x=0 when f(x)=2, then there should be a minimum at x=0, with f(x) being 1/2

 

[umm what]

thanks brahh

the answer to the graphs question is A
i assume you know why it can't be C or D
with B, the graph suggests that 1/f(x) approaches 1 as x approaches infinity. if we look at the original graph, in order for this to be true, f(x) would also need to have a horizontal asymptote at 1. however, this isn't the case. the graph clearly shows that the curve doesn't approach 1 (the line y=1 is shown just to indicate that at x=1 and -1, f(x) = 1 as well)
hence the answer can only be A. as to why the line moves from 1 down to a half, it is to show the turning point of the middle part of the curve (the "parabola") since there was a maximum at x=0 when f(x)=2, then there should be a minimum at x=0, with f(x) being 1/2