Respuesta :

calculista

Answer:

Please see the attached image for your answer

Step-by-step explanation:

If we use a graphing tool or calculator we can easily verify your expresions.

f(x) = x^2

g(x) = 1/(2f(x))

h(x) = (1/2)*f(x)

f(x) and h(x) differ only in their gain.

g(x) tends to zero as x tends to ±∞

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Answer with explanation:

We are given a function f(x) in terms of variable x as:

             [tex]f(x)=x^2[/tex]

  • We know that a transformation of a parent function f(x) of the type:

          f(x) → a f(x)

is either a vertical stretch or a shrink depending on a.

If a>1 then the transformation is a vertical stretch and if a<1 then it is a vertical squeeze.

  • Also, the transformation of the type:

       f(x) → f(ax)

   is a horizontal stretch if a<1 and a horizontal shrink if a>1.

  • Here we have:

               [tex]g(x)=\dfrac{1}{2}f(x)[/tex]

This means that the function g(x) is a vertical shrink of the parent function f(x) since a=1/2 <1

  • Also, we can represent our function as:

       [tex]g(x)=(\dfrac{1}{\sqrt{2}}x)^2[/tex]

This means that:

          [tex]g(x)=f(\dfrac{1}{\sqrt{2}}x)[/tex]

Here we have: a=1/√2 <1

This means that it is a horizontal stretch.

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