Methods Question

[secretweapon]

so since the coefficient of x is 1/4,
and 1 is on the numerator, we only multiply -1*1, as opposed to -1*1/4
Is my understanding correct?
Also, do you know how to find the angle which a graph makes with the positive direction of the X axis?
Thanks

[Springyboy]

so since the coefficient of x is 1/4,
and 1 is on the numerator, we only multiply -1*1, as opposed to -1*1/4
Is my understanding correct?
Also, do you know how to find the angle which a graph makes with the positive direction of the X axis?
Thanks

Yep because this is not differentiation it’s integration so you add one power to the exponent and divide by that power. Since -2+1 = -1 then you only divide by -1 overall which leads to the answer of -1/4x

[Bri MT]

Also, do you know how to find the angle which a graph makes with the positive direction of the X axis?

tan(theta) = opposite/adjacent = rise/run = m

[secretweapon]

Yep because this is not differentiation it’s integration so you add one power to the exponent and divide by that power. Since -2+1 = -1 then you only divide by -1 overall which leads to the answer of -1/4x

But don't you divide by the power and multiply it by the coefficient of x, so in this case 1/4, but how come its multiplied by 1 instead of 1/4?
Thanks

[VanillaRice]

But don't you divide by the power and multiply it by the coefficient of x, so in this case 1/4, but how come its multiplied by 1 instead of 1/4?
Thanks

You do not need to multiply the answer by the coefficient of x - the coefficient simply stays the same. You only need to divide by the "new" power, which in this case is -1.

[secretweapon]

You do not need to multiply the answer by the coefficient of x - the coefficient simply stays the same. You only need to divide by the "new" power, which in this case is -1.

the anti differentiation formula says you have to divide the top part, which is (ax+b)^(n+1) by the bottom part, which is a(n+1)
where a is the coefficient of x?

[VanillaRice]

the anti differentiation formula says you have to divide the top part, which is (ax+b)^(n+1) by the bottom part, which is a(n+1)
where a is the coefficient of x?

That formula only applies for when you have a linear factor raised to a power, and b is non-zero. In this case, want to use the formula located above that on the formula sheet.

[secretweapon]

That formula only applies for when you have a linear factor raised to a power, and b is non-zero. In this case, want to use the formula located above that on the formula sheet.

Thanks looks like i mixed up the formulas, whoops
Also, do you know the most efficient way to prepare for a methods ac in 2 weeks, apart from going over areas of weaknesses?

[VanillaRice]

Thanks looks like i mixed up the formulas, whoops
Also, do you know the most efficient way to prepare for a methods ac in 2 weeks, apart from going over areas of weaknesses?

The most efficient way is the one which works best for you, and can be different for everyone
Other than targeting your weak areas, I would also try to reinforce your stronger concepts - these are the marks which you want to get right.

[secretweapon]

The most efficient way is the one which works best for you, and can be different for everyone
Other than targeting your weak areas, I would also try to reinforce your stronger concepts - these are the marks which you want to get right.

sac, not ac, made a type

[S_R_K]

So the anti-derivative of sin(x) = -cos(x)
Therefore, it'd just be -2cos(x)+k^2/2

As the anti-derivative of k = k^2/2

This response is not correct.

If you anti-differentiate sin(x) + k with respect to x (ie. treating k as a constant), then the anti-derivative is –cos(x) + kx + c.

[Springyboy]

This response is not correct.

If you anti-differentiate sin(x) + k with respect to x (ie. treating k as a constant), then the anti-derivative is –cos(x) + kx + c.

No worries made a mistake when working with that as it's in respect to x

[secretweapon]

h(x) = 1/(x+2)
the above graph undergoes the following transformations:
dilation of factor 1/2 parallel to the x axis, then a translation of 3 units down and 3 units left, then a reflection in the y-axis, followed by a dilation of factor 2 from the x-axis
My final answer ended up being 2/(8-2x)-6, however the books answer was 1/(3-x)-6
Is my answer correct, or the book's answer?
Thanks

[secretweapon]

State the transformations that have been applies to the graph of y = -2(3x-1)^2+5 in order to transform it to the graph of y = (x+2)^2-1

1. reflection in x axis
2. dilation by factor of 1/2 from x axis
3. dilation of factor 3 from y axis
4. translation 2/3 units to the left
5. translation 6 units down
Am i correct?
For the bolded one, the answer sad it was translation of 3 units to left, so is the answer correct, or am I correct?
Thanks

[S_R_K]

h(x) = 1/(x+2)
the above graph undergoes the following transformations:
dilation of factor 1/2 parallel to the x axis, then a translation of 3 units down and 3 units left, then a reflection in the y-axis, followed by a dilation of factor 2 from the x-axis
My final answer ended up being 2/(8-2x)-6, however the books answer was 1/(3-x)-6
Is my answer correct, or the book's answer?
Thanks

The book is wrong. You can also write your answer as .

You can see that the book must be wrong by considering the image of the asymptote x = –2 under the transformations. The dilation by factor 1/2 parallel to the x-axis, followed by a translation by 3 units in the negative direction of the x-axis, followed by a reflection in the y-axis should map the asymptote to x = 4.

State the transformations that have been applies to the graph of y = -2(3x-1)^2+5 in order to transform it to the graph of y = (x+2)^2-1

1. reflection in x axis
2. dilation by factor of 1/2 from x axis
3. dilation of factor 3 from y axis
4. translation 2/3 units to the left
5. translation 6 units down
Am i correct?
For the bolded one, the answer sad it was translation of 3 units to left, so is the answer correct, or am I correct?
Thanks

Yes, it is a translation of 3 units in the negative direction of the x-axis. Once you dilate by a factor of 3 from the y-axis, the turning point at x = 1/3 is mapped to a turning point at x = 1. Then a translation of 3 units in the negative direction of the x-axis is required to map the turning point to x = –2.

Furthermore, the final transformation should be a translation in the positive direction of the y-axis by 3/2 units (notice that when the reflection in the x-axis is applied, the turning point of the original graph will be at y = –5, so the graph must be translated upwards to get a turning point at y = –1. Similarly to above, it is not translated by 4 units because the prior dilation must be taken into account...).