Which statements represent the relationship between y=2x and y=log2x ? Select each correct answer. The functions are inverses of each other. The graphs of the functions are symmetric about the line y = 0. The graphs of the functions are symmetric to each other over the line y = x. The equation y=log2x is the logarithmic form of y=2x .

The given function are inverse of each other.

The graphs of the functions are symmetric to each other over the line y = x.

Given function are,   and  

Therefore, both given function are inverse of each other.

The graphs of the functions are symmetric to each other over the line y = x.

Here, graph is attached below.

From attached graph, it is observed that ,the graphs of the functions are not symmetric about the line y = 0.

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The correct options are;

1) The functions are inverse of each other and

3) The graphs of the functions are symmetric to each other over the line y = x

Step-by-step explanation:

Here we have

y = 2ˣ and y = log₂x

We are to analyze each of the options as follows;

1) The functions are inverse of each other

The above statement is correct as the inverse of y = 2ˣ is x = therefore  y = log₂x is inverse of y = 2ˣ

2) The graphs of the functions are symmetric about the line y = 0

The above statement is not correct as the line y = 0 is the x axis whereby  y = 1 and y = -1 give x = 5 and x = 0.5 respectively

3) The graphs of the functions are symmetric to each other over the line y = x

The line y = x is a straight line with slope = 1  whereby since x >  log₂x, and y > log₂y  then the two lines are symmetric

4) The equation y=log₂x is the logarithmic form of y=2ˣ .

The above statement is not correct as log2ˣ = x log2 ≠  log₂x.

The answer should be A if there is a typo and should be written as:

y = -0.375x + 0.75

Step-by-step explanation:

 3x + 8y = 6

- 3x         - 3x

8y = -3x + 6

y = - 0.375x + 0.75

The answer can't be A nor C.

0.75x + 2y = 1.5

The answer cannot be B

And D is in no way correct