Question

Arrange the transformations of the function y = sec x according to the resultant horizontal shifts, starting from left to right, in the graph of the original secant function. If there are multiple transformations that cause the same horizontal shift, arrange them in ascending order beginning with the lowermost vertical shift.
-3+2sec(4x+2)
-5+3sec(6x-4)
3+0.5sec(2x+1)
-3-5sec(3x-2)
2-0.2sec(5x-2)
-3+1.3sec(x+2)
-1-2sec(6x+5)
-4+7sec(5x-7)

Answer 1

The graph of y=sec(x) is shown in the first diagram

The furthest left horizontal shift happens at sec(6x+5) as it shifts sex(x) five units to the left. Notice that the graph becomes narrower as the effect of $6x$ in the transformation equation. The diagram is shown in the second 

Then the less further equation, sec(x+2) comes next. There are two equation with '$x+2$' but we are interested in the lowest vertical point which is $-3+1.5sec(x+2)$. The graph is given below

The next in order is $-3+2sec(4x+2)$, also a shift of 2 to the left but higher vertical point than the previous equation. This transformation is shown in graph number 4

The next equation is $3+0.5sec(2x+1)$ with a shift of 1 to the left. The graph is shown in graph 5 

The next equation is $2-0.2sec(5x-2)$ with a shift of two units to the right and it has the lowest vertical point (sorry I can't seem to add more graph)

The rest of the equation in order are

$-5+3sec(6x-4)$
$-3-5sec(3x-5)$
$-4+7sec(5x-7)$

Answer 2

1. -3+1.3sec(x+2)

2.-1-2sec(6x+5)

3.-3+2sec(4x+2)

4.3+0.5sec(2x+1)

5.2-0.2sec(5x-2)

6.-5+3sec(6x-4)

7.-3-5sec(3x-2)

8.-4+7sec(5x-7)