Question

2 questions:

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

Answer 1

f(x)=-2 tan(3x - 6)+1 has a negative -2 coefficient out front. negative means reflect vertically across x axis, the 2 is vertical expansion so

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.

question 2:

the amplitude is supposed to be 0.5. but fi you count units from center line y = 3 to a max at y = 5, there is amplitude of 5 - 3 = 2 in the graph.

A. the graph should be compressed vertically instead of expanded

Answer 2

1) A, B 2) A

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.