Question

What transformation has changed the parent function f(x) = (.5)x to its new appearance shown in the graph below?

Answer 1

The transformation that has changed the parent function f(x) to the graph shown is:

f(x+2)

Explanation:

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

`f(x)=(0.5)^x`

and let the transformed function be:

g(x)

Clearly by looking at the graph of the transformed function we observe that:

at x=0

the value of the function lie between 0 and 1.

a)

f(x)-2

i.e. the function is given by:

`g(x)=(0.5)^x-2`

At x=0 we have:

`g(0)=(0.5)^0-2\\\\g(0)=1-2\\\\g(0)=-1`

Hence, option (a) is incorrect.

c)

f(x)+1

`g(x)=(0.5)^x+1`

at x=0 we have:

`g(0)=(0.5)^0+1\\\\g(0)=1+1\\\\g(0)=2`

Hence, option (c) is incorrect.

d)

-1.f(x)

`g(x)=-(0.5)^x`

At x=0 we have:

`g(0)=-(0.5)^0\\\\g(0)=-1`

Hence, option (d) is incorrect.

b)

f(x+2)

`g(x)=(0.5)^(x+2)`

At x=0 we have:

`g(x)=(0.5)^(2)\\\\g(x)=0.25`

Hence, option (b) is the answer.

Answer 2

The graph shown is the graph of f(x) = (0.5)^x shifted two units to the left.
f(x + 2)