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

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

you have to put the graph on here with the question

step-by-step explanation: