The graph of the function f(x)=log5(x) is stretched vertically by a factor of 3, reflected over the x-axis, reflected over the y-axis, and shifted down by 4 units.

Find the equation of the function g(x) described above.

Note: If you are using log you need to type it in and use the subscript button on the keyboard. There is no log button.

Question

High School

Answer :

joaobezerra joaobezerra · Answer 1 · 2024-07-10T01:12:48-04:00

The equation of the function g(x), considering the transformations, is given as follows:

[tex]g(x) = -3\log_5{(-x)} - 4[/tex]

The equation of function g(x) is obtained applying the transformations to the parent function f(x).

The parent function f(x) is given as follows:

f(x) = log5(x).

The vertical stretch by a factor of 3 is represented by a multiplication of f(x) by 3, hence:

g(x) = 3log5(x).

The reflection over the x-axis is represented by a multiplication of the function by -1, hence:

g(x) = -3log5(x).

The reflection over the y-axis is represented by a multiplication by -1 inside the domain of the function, hence:

g(x) = -3log5(-x).

The shift down by four units is represented by a subtraction of the function by four, hence:

g(x) = -3log5(-x) - 4.

Using Latex for better visualization:

[tex]g(x) = -3\log_5{(-x)} - 4[/tex]

More can be learned about transformations at https://brainly.com/question/28792248

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