Question

Which of the following points lies on the graph of the function y=3^x

a.
(1, 0)
c.
(3, 1)
b.
(2, 9)
d.
(0, 3)

Answer 1

b.

(2, 9)

Explanation:

In this problems we have points of the form (
`x_0, y_0`). What we must do is replace each of the points in the function
`y = 3 ^ x`. Replace
`x_0` with x and
`y_0` with y. The point belongs to the function only if the right side of the equality is equal to the left side.

Let's test the point of option a.

to.

(1, 0)

So:

`0 = 3 ^ 1\\0 = 3`

Equality is not met.

If you do the same for all the given points you will see that the only one that belongs to the function is (2, 9)

`9 = 3 ^ 2\\9 = 9`

Finally the correct option is the b

Answer 2

y = 3^x is solved by B

Explanation:

Some of these choices you can do in your head. Some can easily be derived by graphing the question. I 'll try to do both, but the network I'm on may not let me do the graph.

1, 0 obvious won't work. No matter what value of x > 0 the graph won't hit a value of 0 for y. A is incorrect.

C won't work either. If x is 3 then y is never going to be 1. 3^3 is 27.

D Anything to the zero power will never give 3. It should give 1. So D won't work.

The answer has to be B.

3^2 = 9 just as B says. Note I'm using your labeling system.

Notice that three of the points do not fall on the line. Only 1 does and it is the answer.