it is useful to note that for most toolkit functions, a horizontal stretch or vertical stretch can be…

it is useful to note that for most toolkit functions, a horizontal stretch or vertical stretch can be represented in other ways. for example, a horizontal compression of the function $f(x)=x^{2}$ by $1 / 2$ would result in a new function $g(x)=(2 x)^{2}$, but this can also be written as $g(x)=4 x^{2}$, a vertical stretch of $f(x)$ by 4. when writing a formula for a transformed toolkit, we only need to find one transformation that would produce the graph. ? exercise 1.5.7 write a formula for the toolkit square root function $f(x)=sqrt{x}$ horizontally stretched by three. $g(x)=$ question help: message instructor post to forum

it is useful to note that for most toolkit functions, a horizontal stretch or vertical stretch can be represented in other ways. for example, a horizontal compression of the function $f(x)=x^{2}$ by $1 / 2$ would result in a new function $g(x)=(2 x)^{2}$, but this can also be written as $g(x)=4 x^{2}$, a vertical stretch of $f(x)$ by 4. when writing a formula for a transformed toolkit, we only need to find one transformation that would produce the graph. ? exercise 1.5.7 write a formula for the toolkit square root function $f(x)=sqrt{x}$ horizontally stretched by three. $g(x)=$ question help: message instructor post to forum

Answer

Explanation:

Step1: Recall horizontal stretch formula

For a function (y = f(x)), a horizontal stretch by a factor (a) gives (y = f(\frac{x}{a})).

Step2: Apply to square - root function

Given (f(x)=\sqrt{x}) and (a = 3) (horizontal stretch by three), then (g(x)=f(\frac{x}{3})). Substitute (x) with (\frac{x}{3}) in (f(x)): (g(x)=\sqrt{\frac{x}{3}}).

Answer:

(g(x)=\sqrt{\frac{x}{3}})