Using translation concepts, the equations are given as follows:
a) [tex]y = \sqrt{16 - 4x^2}[/tex]
b) [tex]y = 3\sqrt{16 - x^2}[/tex]
What is a translation?
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the parent function is:
[tex]y = \sqrt{16 - x^2}[/tex]
In item a, when it is horizontally compressed by a factor of 2, it means that x -> 2x, hence:
[tex]y = \sqrt{16 - (2x)^2} = \sqrt{16 - 4x^2}[/tex]
In item b, the transformations are given as follows:
- Vertical expansion by a factor of 3, hence y -> 3y.
- Reflected in the y-axis, hence x -> -x.
Then:
[tex]y = 3\sqrt{16 -(-x)^2} = 3\sqrt{16 - x^2}[/tex]
More can be learned about translation concepts at https://brainly.com/question/4521517
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