How do the graphs of the functions f(x) = (Three-halves)x and g(x) = (Two-thirds)x compare?

We want to compare the graphs of the two given functions. We will see that the graph of g(x) is the graph of f(x) reflected across the line y = x.

The given functions are:

f(x) = (3/2)*x

g(x) = (2/3)*x

Note that each point on the line f(x) is written as:

(x, (3/2)*x)

And each point on the line g(x) is written as:

(x, (2/3)*x)

Now, if we multiply both sides of the above point by (3/2) we will get:

((3/2)*x, x)

Now, remember that for a general point (x, y), if we apply reflection across the line y = x, we get.

(y, x)

So the order of the values changes, exactly as we can see for f(x) and g(x).

Then we can conclude that g(x) is obtained by reflection f(x) across the line y = x.

Then the graph of g(x) is the graph of f(x) reflected across the line y = x.

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The answer to this question can be defined as follows:

Step-by-step explanation:

Given:

Following are the graph attachment to this question:

The second function, that is is not even a function.

Remember that g(x) function is the inverted f(x) function. And when you see this pattern, a reflection on the Y-axis expects you.

Reflection in the axis.

In x-axis:

Increase the function performance by -1 to represent an exponential curve around the x-axis.

In y-axis:

Increase the input of the function by -1 to represent the exponential function around the y-axis.