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Answer 1

Using translation concepts, the equation of g(x) is given as follows:

$g(x) = -\frac{35}{x + 10} - 1$

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.

For this problem, the parent function is given by:

$f(x) = \frac{1}{x}$

For a horizontal compression by a factor of 1/5, we have to find f(1/5x), hence:

$g(x) = \frac{1}{\frac{1}{5}}x = \frac{5}{x}$

For a vertical stretch by a factor of 7, we have to multiply by 7, hence:

$g(x) = \frac{35}{x}$

For a reflection in the y-axis, we have to find g(-x), hence:

$g(x) = \frac{35}{-x} = -\frac{35}{x}$

For a translation of 10 units left, we have to find g(x + 10), hence:

$g(x) = -\frac{35}{x + 10}$

For a translation of 1 unit down, we have to subtract one, hence:

$g(x) = -\frac{35}{x + 10} - 1$

More can be learned about translation concepts at brainly.com/question/28174785

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