Answer:
B
Step-by-step explanation:
Look at the graph, it passes to (0,3), so you need to replace that coordinate into A,B,C,D. Then you can see, there is only B and C satisfies.
[tex]Y=3(\frac{1}{3} )^{0}=3.1=3.[/tex]
and
[tex]Y=(\frac{1}{2} )^{0}+2=1+2=3[/tex]
Next step, you can see when x approach to infinite then Y approach to 0.
Hence, we will take limit of B and C, if limit B or C equals to 0 then we will choose.
[tex]\lim_{x \to \infty} {3(\frac{1}{3})^x=3. \lim_{x \to \infty} {(\frac{1}{3})^x=3.0=0[/tex]
and
[tex]\lim_{x \to \infty} {[(\frac{1}{2})^x+2]}= \lim_{x \to \infty} {(\frac{1}{2})^x}+ \lim_{x \to \infty} {2}=0+2=2[/tex]
We can see that only B is satisfied.
