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.

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