# helppppppppp

Watch
Announcements

Page 1 of 1

Go to first unread

Skip to page:

sorry, I cannot attach a photo...there is a question about math:

a curve with equation y=sin(ax-b),where a>0,0<b<pi,the curve cuts x-axis at P,Q,R as shown, givenP(pi/10,0),R（3pi/5,0）,R(11pi/10,0），find a and b.

the answer is a=2,b=pi/5, and they made a simultaneous equation :a pi/10-b=0 and a3pi/5-b=0,and got the answers.

but I wonder if a and b represents change of graph, then they should follow the role 'f(ax+b) means the x-coordinate of the points divided by a and minus b,which is opposite...I am confused why the answer just simply substitute the coordinates into ax-b,without times a becomes divided by a,minus b become plus b.

I am really thankful if anyone could explain to me about this

a curve with equation y=sin(ax-b),where a>0,0<b<pi,the curve cuts x-axis at P,Q,R as shown, givenP(pi/10,0),R（3pi/5,0）,R(11pi/10,0），find a and b.

the answer is a=2,b=pi/5, and they made a simultaneous equation :a pi/10-b=0 and a3pi/5-b=0,and got the answers.

but I wonder if a and b represents change of graph, then they should follow the role 'f(ax+b) means the x-coordinate of the points divided by a and minus b,which is opposite...I am confused why the answer just simply substitute the coordinates into ax-b,without times a becomes divided by a,minus b become plus b.

I am really thankful if anyone could explain to me about this

0

reply

Report

#2

(Original post by

sorry, I cannot attach a photo...there is a question about math:

a curve with equation y=sin(ax-b),where a>0,0<b<pi,the curve cuts x-axis at P,Q,R as shown, givenP(pi/10,0),R（3pi/5,0）,R(11pi/10,0），find a and b.

the answer is a=2,b=pi/5, and they made a simultaneous equation :a pi/10-b=0 and a3pi/5-b=0,and got the answers.

but I wonder if a and b represents change of graph, then they should follow the role 'f(ax+b) means the x-coordinate of the points divided by a and minus b,which is opposite...I am confused why the answer just simply substitute the coordinates into ax-b,without times a becomes divided by a,minus b become plus b.

I am really thankful if anyone could explain to me about this

**Wuxinyu**)sorry, I cannot attach a photo...there is a question about math:

a curve with equation y=sin(ax-b),where a>0,0<b<pi,the curve cuts x-axis at P,Q,R as shown, givenP(pi/10,0),R（3pi/5,0）,R(11pi/10,0），find a and b.

the answer is a=2,b=pi/5, and they made a simultaneous equation :a pi/10-b=0 and a3pi/5-b=0,and got the answers.

but I wonder if a and b represents change of graph, then they should follow the role 'f(ax+b) means the x-coordinate of the points divided by a and minus b,which is opposite...I am confused why the answer just simply substitute the coordinates into ax-b,without times a becomes divided by a,minus b become plus b.

I am really thankful if anyone could explain to me about this

**a3pi/5-b=0**do you really mean for it to be zero on the RHS? [Never mind, I have found an image online]

Note that is a transformation of . It represents a horizontal translation to the right by units, followed by a horizontal stretch with scale factor . (See spoiler below for why)

Notice that are the first three consecutive roots of , whereas the first three consecutive roots of are .

So, you can approach this problem by imagining that transforms into , and then transforms into , and transforms into .

Take the first case. We begin with 0 and the first step is a stretch to the right by units. This means and this is our new coordinate. Then we stretch by scale factor and obtain .

Thus, this is our final new coordinate, and it corresponds to .

Hence, and you can rearrange this into .

Repeating similarly by transforming to yields .

Spoiler:

Consider the function being transformed into . We aim to understand why this is precisely a horizontal shift to the right by b units followed by a horizontal stretch with scale factor 1/a.

Take a single point on , let's say is a point. Hence, the equation is satisfied.

Now, we seek the transformed point for which lies on our *new* curve. Hence, the equation (*) is satisfied. Note that we can impose the condition that (**), because then hence the equation (*) certainly holds! So, rearrange (**) for to get .

So what we have found is that our new coordinate X' in relation to the old coordinate X is simply a shift to the right by units (represented by +b) and then stretched by factor .

Hence, takes on values values which have been shifted to the right by b units, and stretched by factor 1/a as compared to the original function .

Show

Consider the function being transformed into . We aim to understand why this is precisely a horizontal shift to the right by b units followed by a horizontal stretch with scale factor 1/a.

Take a single point on , let's say is a point. Hence, the equation is satisfied.

Now, we seek the transformed point for which lies on our *new* curve. Hence, the equation (*) is satisfied. Note that we can impose the condition that (**), because then hence the equation (*) certainly holds! So, rearrange (**) for to get .

So what we have found is that our new coordinate X' in relation to the old coordinate X is simply a shift to the right by units (represented by +b) and then stretched by factor .

Hence, takes on values values which have been shifted to the right by b units, and stretched by factor 1/a as compared to the original function .

Last edited by RDKGames; 10 months ago

1

reply

thank you, but I cannot understand why f(ax+b）means b units to the left,why not right, I just treated it as a rule before and do not understand it actually.

0

reply

Report

#4

(Original post by

thank you, but I cannot understand why f(ax+b）means b units to the left,why not right, I just treated it as a rule before and do not understand it actually.

**Wuxinyu**)thank you, but I cannot understand why f(ax+b）means b units to the left,why not right, I just treated it as a rule before and do not understand it actually.

To make it easier to understand, draw the graph of y =x, y=x+1 and y=x-!. You will see what I'm talking about...

0

reply

(Original post by

What is the diagram they post? Also, for

**RDKGames**)What is the diagram they post? Also, for

**a3pi/5-b=0**do you really mean for it to be zero on the RHS?
0

reply

Report

#6

(Original post by

yes, I do

**Wuxinyu**)yes, I do

but why it must be (0+b)/a,not 0/a+b to strech first then shift?

being shifted, then stretched yields .

being stretched, then shifted yield .

So there is a difference!

Last edited by RDKGames; 10 months ago

0

reply

Report

#7

(Original post by

thank you, but I cannot understand why f(ax+b）means b units to the left,why not right

**Wuxinyu**)thank you, but I cannot understand why f(ax+b）means b units to the left,why not right

0

reply

X

Page 1 of 1

Go to first unread

Skip to page:

### Quick Reply

Back

to top

to top