Using translation concepts, it is found that the transformations necessary to transform the graph of f(x) into that of g(x) are given as follows:
- Reflection over the y-axis.
- Horizontal stretch by a factor of 2.
- Reflection over the x-axis.
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.
The original function f(x) is given by:
[tex]f(x) = \sqrt{x}[/tex]
The transformations are as follows:
- Inside the domain, the function was multiplied by -1/2 and 3 was added. Hence the function was reflected over the y-axis, horizontally stretched by a factor of 2 and shifted left 3 units.
- Outside the domain, in the range, the function was multiplied by -1 and 1 was subtracted, hence the function was reflected over the x-axis and shifted down one unit.
More can be learned about translation concepts at https://brainly.com/question/4521517
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