Using translation concepts, the equation of g(x) is given as follows:
[tex]g(x) = -\frac{35}{x + 10} - 1[/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.
For this problem, the parent function is given by:
[tex]f(x) = \frac{1}{x}[/tex]
For a horizontal compression by a factor of 1/5, we have to find f(1/5x), hence:
[tex]g(x) = \frac{1}{\frac{1}{5}}x = \frac{5}{x}[/tex]
For a vertical stretch by a factor of 7, we have to multiply by 7, hence:
[tex]g(x) = \frac{35}{x}[/tex]
For a reflection in the y-axis, we have to find g(-x), hence:
[tex]g(x) = \frac{35}{-x} = -\frac{35}{x}[/tex]
For a translation of 10 units left, we have to find g(x + 10), hence:
[tex]g(x) = -\frac{35}{x + 10}[/tex]
For a translation of 1 unit down, we have to subtract one, hence:
[tex]g(x) = -\frac{35}{x + 10} - 1[/tex]
More can be learned about translation concepts at https://brainly.com/question/28174785
#SPJ1
