Question

How would you describe the difference between the graphs of and ?A.g(y) is a reflection of f(x) over the line y = 1.B.g(y) is a reflection of f(x) over the y-axis.C.g(y) is a reflection of f(x) over the x-axis.D.g(y) is a reflection of f(x) over the line y = x.

Answer 1

Explanation:

We are given function f(x):

`f(x)=x^2+4`

And a transformed function:

`g(y)=y^2+4`

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:

`\begin{gathered} (x,y) \\ \downarrow \\ (y,x) \\ \downarrow \\ \boxed{Reflection\text{ across the line y=x}} \end{gathered}`

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