Triangle △ABC is in the first quadrant and translated along ‹ 8, 6 › and reflected across the x-axis. Which quadrant will the triangle be in after the first transformation? Which quadrant will the triangle be in after the second transformation?

The triangle will be in the first quadrant after the 1st transformation

The triangle will be in the fourth quadrant after the 2nd transformation

Step-by-step explanation:

* Lets revise translation and reflection

- Horizontal translation means move the figure to right or to left

- Vertical translation means move the figure up or down

- Reflection across x-axis reverses the figure from up the x-axis to

down the x-axis or reverses it from down the x-axis to up the x-axis

* Lets solve the problem

- Triangle △ABC is in the first quadrant

- It translated along ‹ 3, 7 ›

- Then reflected across the x-axis

- We need to know the image of the triangle after first transformation

lies in which quadrant and after the second transformation lies in

which quadrant

∵ The triangle in first quadrant

∵ The translation is <3 , 7>

- That means the triangle is translated 3 units to the right and

 7 units up

∴ The triangle still in the first quadrant

* The triangle will be in the first quadrant after the 1st transformation

∵ The triangle reflected across the x-axis

- That means the triangle is reversed from up the x-axis to down

the x-axis

∴ The triangle is reversed to the fourth quadrant

* The triangle will be in the fourth quadrant after the 2nd transform

the opening of this porabola is facing up

step-by-step explanation:

asnwer is (g o h o f)(x) = 2x - 6/x + 7

step-by-step explanation:

given,

f(x) = x - 3/x

g(x) = x + 3

h(x) = 2x + 1

we need to find : (g o h o f)(x)

we can write (g o h o f)(x) = g[ h{ f(x) } ]

so first we find h{f(x)}

h{f(x)} = f(x) + 3 = (x - 3/x) + 3

h{f(x)} = x - 3/x + 3

now we find g[ h{ f(x) } ].

g[ h{ f(x) } ] = g(x - 3/x + 3)       {plug h{f(x)} = x - 3/x + 3 in g[h{f(x)}] }

g(x - 3/x + 3) = 2 (x - 3/x + 3) + 1

                    = 2x - 6/x + 6 + 1

                    = 2x - 6/x + 7

hence we get (g o h o f)(x) = 2x - 6/x + 7