Question

Which function is shown in the graph below?

Answer 1

the annswer is y=log3x

Answer 2

Option C.

Explanation:

There are three points which are passing through the logarithmic function shown in the graph.

The points are (0.4, -0.6), (1, 0) and (3, 1).

Now we will plug in the values (3, 1) in all the options to get the correct answer.

a).
`y=log_(0.4)x`

We can rewrite the equation as

`(0.4)^(y)=x` [If
`a^(b)=c` then
`b=log_(a)c`]

For (3, 1)

`(0.4)^(1)=3`

Which is not true so option A is not the answer.

b).
`y=log_(1)x`

We can rewrite the equation as

`(1)^(y)=x`

For (3, 1)

`(1)^(3)=3`

1 = 3

Which is not true.

Therefore, Option B is not the answer.

c).
`y=log_(3)x`

We can rewrite the equation as

`(3)^(y)=x`

For (3, 1)

`(3)^(1)=3`

3 = 3

Therefore, option C is the answer.

d).
`y=log_(10)x`

We can rewrite the equation as

`(10)^(y)=x`

For (3, 1)

`(10)^(1)=3`

Not true. Therefore, option D is not the answer.