Question

Which of the following describes the transformation of g(x)=3(2)^-x+2 from the parent function f(x)=2^x?
reflect across the x-axis, stretch the graph vertically by a factor of 3, shift 2 units up
reflect across the y-axis, stretch the graph vertically by a factor of 2, shift 3 units up
reflect across the x-axis, stretch the graph vertically by a factor of 2, shift 3 units up
reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up

Answer 1

The last option.

Reflection with y: x -> -x

Stretch vertically: Factor of 3

Shift up : 2 units

Answer 2

The transformation of  $g(x)=3(2)^{-x}+2$  from the parent function  $f(x) = 2^x$  will be carried out by reflecting f(x) across the y-axis, then stretch the graph of f(x) vertically by a factor of 3 and then shift 2 units up,

Given :

Transforation Function - $g(x)=3(2)^{-x}+2$

Parent Function - $f(x) = 2^x$

To convert parent function into transformation function following steps can be used:

Step 1 - Multiply 3 to the function f(x). Due to this the graph of f(x) shift by vertically by 3 units.

$f(x) = 3(2)^x$

Step 2 - Now, replace x with -x. Due to this the graph of f(x) reflects about y-axis.

$f(x)=3(2)^{-x}$

Step 1 - Add 2 to the function f(x). Due to this the graph of f(x) shift by two units.

$f(x) =3( 2)^{-x}+2 = g(x)$

From the above steps it can be concluded that option D) is correct.

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https://brainly.com/question/10712002