Respuesta :

Answer:

1. Line A

2. Line B

3. Line C

Step-by-step explanation:

The parent function of the given functions can be taken : 'f(x) = log_2(x)'. The function r(x) is vertically stretched version of its parent function by a factor of '4' and flipped upside down, and the function s(x) is the origin shifted(to the right) by 2 units version of its parent function.

How does transformation of a function happens?

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:

Horizontal shift (also called phase shift):

  • Left shift by c units: [tex]y=f(x+c)[/tex] (same output, but c units earlier)
  • Right shift by c units:  [tex]y=f(x-c)[/tex] (same output, but c units late)

Vertical shift:

  • Up by d units: [tex]y = f(x) + d[/tex]
  • Down by d units: [tex]y = f(x) - d[/tex]

Stretching:

  • Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]
  • Horizontal stretch by a factor k: [tex]y = f\left(\dfrac{x}{k}\right)[/tex]

The function given are:

  • [tex]r(x) = -4\log_2(x)[/tex], and
  • [tex]s(x) = \log_2(x-2)[/tex]

If we take the parent function of these functions as:

[tex]f(x) = \log_2(x)[/tex]

Then, as we have:

[tex]r(x) = -4\log_2(x) = -4 f(x)[/tex]

Thus, r(x) is vertically streched version of its parent function by scale factor 4.

That negative sign just flips the outputs.

Also, as we've got:

[tex]s(x) = \log_2(x-2) = f(x-2)[/tex]

Thus, s(x) is right shifted version of iits parent function f(x) by 2 units.

Their graphs is attached below.

Thus, the parent function of the functions r(x) = -4 log_2(x), and s(x) = log_2 (x - 2) can be taken " f(x) = log_2(x) '. The function r(x) is vertically stretched version of its parent function by a factor of '-4', and the function s(x) is the origin shifted(to the right) by 2 units version of its parent function.

Learn more about transforming functions here:

https://brainly.com/question/17006186

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