Which of the following describes the transformation of g (x) = 3 (2) superscript negative x baseline + 2 from the parent function f (x) = 2 superscript x?
reflect across the x-axis, stretch the graph vertically by a factor of 3, shift 2 units up
reflect across the y-axis, stretch the graph vertically by a factor of 2, shift 3 units up
reflect across the x-axis, stretch the graph vertically by a factor of 2, shift 3 units up
reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up

Option d: reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up.

Step-by-step explanation:

The parent function is

The transformation function is

In the transformed function, the function is added +2, which shifts the graph by 2 units up.

Also, the function is multiplied by 3, which stretches the function  vertically by a factor of 3 units.

The variable x is multiplied by -1, such that the function reflects across y-axis.

Thus, the correct answer is option d.

The graph is attached below which shows the parent function and the transformed function.

The transformation function is reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up.

$32,660

step-by-step explanation:

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18