The functions 𝑓 and 𝑔 are defined for all real numbers such that 𝑔⁡(𝑥)=𝑓⁡(2⁢(𝑥-4)). Which of the following sequences of transformations maps the graph of 𝑓 to the graph of 𝑔 in the same 𝑥⁢𝑦-plane?

How does the graph of 𝑓(𝑥)=−32𝑥−4f(x)=−3 2x −4 differ from the graph of 𝑔(𝑥)=−32𝑥g(x)=−3 2x ?A.The graph of 𝑓(𝑥)f(x) is shifted four units to the right of the graph of 𝑔(𝑥)g(x).B.The graph of 𝑓(𝑥)f(x) is shifted four units down from the graph of 𝑔(𝑥)g(x).C.The graph of 𝑓(𝑥)f(x) is shifted four units up from the graph of 𝑔(𝑥)g(x).D.The graph of 𝑓(𝑥)f(x) is shifted four units to the left of the graph of 𝑔(𝑥)g(x).SUBMITarrow_backPREVIOUS

Describe the sequence of transformations that are required to graph based on .a.)The graph is shifted to the right by 5 units, reflected around the x-axis, stretched vertically, and shifted up 12 units.b.)The graph is shifted to the right by 5 units, stretched vertically, and shifted up 12 units.c.)The graph is shifted to the left by 5 units, reflected around the x-axis, stretched vertically, and shifted up 12 units.d.)The graph is shifted to the right by 5 units, reflected around the x-axis, stretched vertically, and shifted down 12 units.

The function 𝑓(𝑥) is transformed to 𝑔(𝑥) by a horizontal shift by 𝑎 units to the left and vertical stretch  by 𝑏 units.Under this transformation, a point 𝐴(2,1) on the graph of 𝑓(𝑥) is transformed to a point 𝐵(0,3) on the graph of 𝑔(𝑥).Find the transformed function 𝑔(𝑥).

The graph of the parent function, f(x) = x3, is translated such that the function g(x) = (x – 4)3 – 1 represents the new graph. Which transformations occurred? Horizontal translation: Vertical translation:

Identify the correct function for the graph shown.  Group of answer choices𝑓(𝑥)=11𝑥+4 𝑓(𝑥)=4𝑥−1 𝑓(𝑥)=14𝑥−1 𝑓(𝑥)=4𝑥+1 𝑓(𝑥)=14𝑥+1