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please help! The function, f(x) = x2, is transformed to obtain function g as shown.


g(x)=0.2(x+3)^{2}-5


Which statement correctly describes the graph of function g?

A. It is the graph of f(x) = x2 vertically stretched, and then translated 5 units down and 3 units to the left.

B. It is the graph of f(x) = x2 vertically compressed, and then translated 5 units down and 3 units to the left.

C. It is the graph of f(x) = x2 vertically compressed, and then translated 3 units up and 5 units to the right.

D. It is the graph of f(x) = x2 vertically stretched, and then translated 3 units up and 5 units to the right.

Respuesta :

Answer:

The statement that correctly describes the graph of function g is:

           B. It is the graph of f(x) = x² ; vertically compressed, and then translated 5 units down and 3 units to the left.  

Step-by-step explanation:

We are given a parent function f(x) as:

        [tex]f(x)=x^2[/tex]

Also, the transformed function g(x) is given by:

        [tex]g(x)=0.2\times (x+3)^2-5[/tex]

We know that the transformation of the type:

  • f(x) → a f(x) gives a vertical stretch or compression depending on a.

If 0<a<1 then the transformation is a vertical compression

and if a>1 then it is a vertical stretch.

Here we have:  a=0.2<1

Hence, the transformation is a vertical compression.

  • Also, the transformation of the type:

      f(x) → f(x+a)

shifts the graph to the left or right by a units depending whether a>0 or a<0

If a>0 then the shift is a units to the left and if a<0 then the shift is a units to the right.

Here we have: a=3>0

Hence, the shift is 3 units to the left.

  • and also the transformation of the type:

         f(x) → f(x)+k

is a shift of the function f(x) either up or down depending on whether k is positive or negative.

If k>0 then the shift is k units upward.

and if k<0 then the shift is k units downward.

          Hence, the answer is:

             Option: B

Using translation concepts, it is found that the correct option is:

B. It is the graph of [tex]f(x) = x^2[/tex] vertically compressed, and then translated 5 units down and 3 units to the left.

The parent function is:

[tex]f(x) = x^2[/tex]

First, it is multiplied by 0.2, which is a number less than 1, meaning it was vertically compressed.

Then, [tex]x \rightarrow x + 3[/tex], which means that the function was shifted 3 units to the left.

Then, 5 was subtracted, which means that the function was shifted 5 units down.

A similar problem is given at https://brainly.com/question/4521517

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