f(x)= 1/x, vertically stretched by a factor of 7, reflected in the y-axis, translated 5 units to the right, and translated 3 units downward.

First off, to reflect an equation in the y axis, just multiply by -1. Now that it is reflected, to stretch an equation by a factor of 7, multiply it by 7. Now we have -7/x.

Then, to move an equation down by 3 units, simply subtract it by 3. Now we have -7/x - 3.

Lastly, since you want to translate it 5 units to the left, you want the equation to be undefined at x = 5 (because originally it is undefined at x = 0). To do that, set the denominator to x - 5. We arrive at our answer: -7/(x-5) - 3.

joaobezerra joaobezerra · Answer 2 · 2021-10-07T12:27:58+02:00

Using translation concepts, it is found that the new definition for the function is:

[tex]g(x) = -\frac{7}{x - 5} - 3[/tex]

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The parent function is:

[tex]f(x) = \frac{1}{x}[/tex]

A vertical stretch by a factor of a means that the function is multiplied by a.
Factor of 7, thus:

[tex]g(x) = 7 \times \frac{1}{x} = \frac{7}{x}[/tex]

Reflection over the y-axis means that we have g(-x), thus:

[tex]g(-x) = \frac{7}{-x} = -\frac{7}{x}[/tex]

Translating a units to the right is g(x - a), 5 units, thus:

[tex]g(x) = -\frac{7}{x - 5}[/tex]

a units downward means that a is subtracted from the function, 3 units, thus:

[tex]g(x) = -\frac{7}{x - 5} - 3[/tex]

A similar problem is given at https://brainly.com/question/19383602