Question

A. Y = 1/3(3)^x B. Y= 3(1/3)^x C. Y= (1/2)^x +2 D. Y=(2)^x - 1

Answer 1

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.

$Y=3(\frac{1}{3} )^{0}=3.1=3.$

and

$Y=(\frac{1}{2} )^{0}+2=1+2=3$

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.

$\lim_{x \to \infty} {3(\frac{1}{3})^x=3. \lim_{x \to \infty} {(\frac{1}{3})^x=3.0=0$

and

$\lim_{x \to \infty} {[(\frac{1}{2})^x+2]}= \lim_{x \to \infty} {(\frac{1}{2})^x}+ \lim_{x \to \infty} {2}=0+2=2$

We can see that only B is satisfied.