Methods Question

[secretweapon]

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.

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...).

but 3(x-1/3) to (x+2)
2+ 1/3 = 7/3 = 2.33333
confused

[S_R_K]

but 3(x-1/3) to (x+2)
2+ 1/3 = 7/3 = 2.33333
confused

I don't see the relevance of that calculation.

The simplest way is to set 3x – 1 = x' + 2, and solve for x'. This gives the correct translation.

[secretweapon]

Using matrix methods, find the image of the point (-2,5) under the following sets of transformations.
Dilation of factor 2 from y-axis, reflection in the y axis, then a shift down 2 units
How do we know which order to multiply the matrices?

Maths quest 12 textbook
exercise 3.4
question 10.
Does anyone with the maths quest text book know how to do this?
(the transformation part of the matrix is in brackets)
[[x'],[y']] = [[-1,0],[0,3]] ([

• ,[y]]+[[1],[0]])

Thanks

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

so for the equation y = -x+1
tan(theta) = -1
when i solve for theta in my cas, it says no solution?

MOD EDIT: Merged triple post