Using translation concepts, the equation of the function in item 40 is:
[tex]f(x) = \sqrt{x + 2} - 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 either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In item 40, the parent function is:
[tex]y = \sqrt{x}[/tex]
The changes are:
- Translation of 2 units down, hence y = y - 2.
- Translation of 2 units left, hence x -> x + 2.
Thus, the rule is:
[tex]f(x) = \sqrt{x + 2} - 2[/tex]
More can be learned about translation concepts at https://brainly.com/question/4521517
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