Respuesta :
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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