Which describes the difference between the graph of f(x) = 2x^3 - 8x + 3 and g(x) = x^3 - 4x?
A) The graph of g(x) is obtained by shifting f(x) up 3 units and stretching vertically by a factor of 2.
B) The graph of f(x) is obtained by shifting g(x) up 3 units and stretching vertically by a factor of 2.
C) The graph of g(x) is obtained by shifting f(x) right 3 units and compressing vertically by a factor of 2.
D) The graph of f(x) is obtained by shifting g(x) right 3 units and compressing vertically by a factor of 2.

Question

Which describes the difference between the graph of f(x) = 2x^3 - 8x + 3 and g(x) = x^3 - 4x?
A)	The graph of g(x) is obtained by shifting f(x) up 3 units and stretching vertically by a factor of 2.	
B)	The graph of f(x) is obtained by shifting g(x) up 3 units and stretching vertically by a factor of 2.	
C)	The graph of g(x) is obtained by shifting f(x) right 3 units and compressing vertically by a factor of 2.	
D)	The graph of f(x) is obtained by shifting g(x) right 3 units and compressing vertically by a factor of 2.

mathmale · Answer

Once you understand the concept of vertical stretching / compression, this problem appears to be not so hard.

What are your thoughts so far?

Is there any similarity between g(x) and f(x)?  If so, what is that similarity?