Question

Which function is shown in the graph below?

Answer 1

Answer:

Option C.

Step-by-step 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.

Answer 2

The annswer is y=log3x