The parent function, f(x)=5^x has been vertically compressed by a factor of one-half shifted to the right three units and down two units. choose the correct function to represent the transformation

The required function is .

Step-by-step explanation:

The given parent function is

The transformation of a parent function is defined as

Where, k represents the vertical stretch or compression, a represents the horizontal shift and b represent the vertical shift.

→ If |k|>1, then it represents vertically stretch and If |k|<1, then it represent vertically compression.

→ If a>0, then f(x) shifts left by a units and If a<0, then f(x) shifts right by a units.

→If b>0, then f(x) shifts upward by b units and If b<0, then f(x) shifts downward by b units.

Since the graph of f(x) has been vertically compressed by a factor of one-half shifted to the right three units and down two units.

The graph of required function is

Therefore the required function is .

Function transformation involves changing the form of a function

The function that represents the transformation is: g(x) = 1/2(5^(x -3))

The parent function is given as:

f(x) = 5^x

When the function is vertically compressed by a factor of one-half, the function becomes

f'(x) = 1/2(5^x)

When the function is shifted 3 units right, it becomes

f"(x) = 1/2(5^(x -3))

Rewrite the function as:

g(x) = 1/2(5^(x -3))

Hence, the function that represents the transformation is: g(x) = 1/2(5^(x -3))

Read more about function transformation at:

link

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)