2questions:

1. which of the following statements are true about the graph of f(x)=-2 tan(3x - 6)+1? select all that apply.

a. it is a vertical shift of the parent function up 1 unit.
b. it is a reflection of the parent functi0on across the x-axis.
c. it is a vertical expansion of the parent function by a factor of 2.
d. it is a horizontal shift of the parent function 1/2 left.
e. it is a horizontal expansion of the parent function by a factor of 3

(the second question is in the attatchment

1) A, B 2) A

Step-by-step explanation:

To answer it properly we've got to check at first, the parent function y=atan(x)+q,  like this y=tan(x).

1)

1. For any trigonometric function that can be written as

f(x)= A.g(x)(Bx-C)+D, The Vertical Phase Shift is given by D. So replacing the letters for the values in this function y=-2tan(3x-6)+1 We have D=1. So in this function, there's a vertical shift up 1 unit for, in comparison to y=tan(x), its parent function. Then, A, it's correct.

1d. The -2 points out a reflection over y=axis. For all a<0 on y=atan(x)+q reflects the graph over the x-axis. So B is true.

2) Looking attentively at y=0.5sin(2x-1)+3.

The Original graph should be vertically "shorter" i.e., compressed than this one, so the Range would be graphed as 2.5≤ y ≤ 3.5, and not as 1 ≤ y ≤4 like it is wrongly graphed.

Furthermore, since 0.5 > 0 the vertical shift is up, and D=3, D>0 the horizontal shift is supposed to be on the right.

Therefore, the true answer is also A.

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d