Explanation:
We are given function f(x):
[tex]f(x)=x^2+4[/tex]
And a transformed function:
[tex]g(y)=y^2+4[/tex]
The difference between these two functions is that in g(x) the variable x was replaced by the variable y. This can be described by the transformation:
[tex]\begin{gathered} (x,y) \\ \downarrow \\ (y,x) \\ \downarrow \\ \boxed{Reflection\text{ across the line y=x}} \end{gathered}[/tex]
Which represents a reflection across line y=x.
This can also be seen with the graph of the two functions:
• f(x) is in blue,
,
• g(x) is in green,
,
• line y=x is in purple
g(x) is a reflection across line y=x of f(x).
Answer:
D. g(x) is a reflection of f(x) over the line y=x
