Answer:
The transformation that has changed the parent function f(x) to the graph shown is:
f(x+2)
Step-by-step 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.
