Question

Describe the transformations necessary to transform the graph of f(x) into that of g(x).

Answer 1

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.

• Shift left 3 units.

• Reflection over the x-axis.

• Shift down 1 unit.

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:

$f(x) = \sqrt{x}$

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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