Let f(x)=3^x . which function represents a transformation of f(x) by a vertical stretch with factor 6? g(x)=1/6 ⋅ 3^x g(x)=3^1/6x g(x)=3^6x g(x)=6 ⋅ 3^x let f(x)=5^x . let g(x)= 5^x − 7 . which statement describes the graph of g(x) with respect to the graph of f(x) ? a. g(x) is translated 7 units left from f(x) . b. g(x) is translated 7 units up from f(x) . c. g(x) is translated 7 units right from f(x) . d. g(x) is translated 7 units down from f(x) .

Ques 1)

Ques 2)

          D.      g(x) is translated 7 units down from f(x) .

Ques 1)

We know that the transformation of the type:

  f(x) → a f(x)

is a vertical compression or stretch depending on a.

If a>1 then we have a vertical stretch by a factor of a.

If 0<a<1 then we have a vertical compression.

Here we have a function f(x) as:

Now, if it is vertically stretched by a factor of 6 then the transformed function g(x) is given by:

Ques 2)

We know that the transformation of the type:

        f(x) → f(x)+a

is a shift i.e. translation of the function f(x) either a units up or a units down depending on a.

If a>0 then the shift is a units up.

if a<0 then the shift is a units down.

Here the function f(x) is:

and the transformed function g(x) is:

Since a= -7<0

Hence, the shift is 7 units down.

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step-by-step explanation: vsfdvsfvd