Select the correct graph of the function given by $f ( x ) = x ^ { 4 }$ . Explain how the graph of function g differs (if it does) from the graph of each function $f$. $g ( x ) = f ( x ) + 8$
A) Horizontal shift of eight units to the left
B) Vertical shift of eight units
C) Horizontal shift of eight units to the right
D) Vertically downward shift of eight units
E) Horizontal shift of eight units

Question

Select the correct graph of the function given by $f ( x ) = x ^ { 4 }$ . Explain how the graph of function g differs (if it does) from the graph of each function $f$. $g ( x ) = f ( x ) + 8$ 
A) Horizontal shift of eight units to the left 
B) Vertical shift of eight units 
C) Horizontal shift of eight units to the right 
D) Vertically downward shift of eight units 
E) Horizontal shift of eight units

Quizplus · Accepted Answer

The graph of function g is identical to the graph of function f, except that it is shifted vertically upward by 8 units. This is because function f is simply a fourth-degree polynomial function, which is a smooth curve that passes through the origin and is symmetric about the y-axis. Adding a constant to this function shifts the entire graph upward or downward without changing its shape or symmetry. In this case, adding 8 to f(x) shifts the graph vertically upward by eight units, which is shown in choice B.

Select the Correct Graph of the Function Given By f(x)=x4f ( x ) = x ^ { 4 }f(x)=x4

Select the Correct Graph of the Function Given By $f ( x ) = x ^ { 4 }$