Question

How would you describe the difference between the graphs of f(x)=x^2 + 4 and g(y)=y^2+4?

A. g(y) is a reflection of f(x) over the line y=x.

B. g(y) is a reflection of f(x) over the x-axis.

C. g(y) is a reflection of f(x) over the y-axis.

D. g(y) is a reflection of f(x) over the line y=1.

Answer 1

the x and y are 'swapped. so we have

a reflection over the line y=x

Answer 2

Option: A is the correct answer.

A. g(y) is a reflection of f(x) over the line y=x.

Explanation:

We know that the reflection of a parent function f(x) about the line y=x is such that the x and the y-values change places i.e. there is a swap in the x and y variables.

Here we are given a parent function f(x) as:

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

Also, the function g(y) is given by:

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

Clearly we could see that the x and the y-variables are swapped.

Hence, the transformation g(y) is a reflection of f(x) over the line y=x.