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.

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

B. It is the graph of vertically compressed, and then translated 5 units down and 3 units to the left.

The parent function is:

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

Then, , 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 link

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.  

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

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

We know that the transformation of the type:

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.

      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.

         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

(x, y)→(x − 8, y − 7)

step-by-step explanation:

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