Question

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

Answer 1

Answer:

The answer to this question can be defined as follows:

Step-by-step explanation:

Given:

$\bold{f(x)= (\frac{3}{2})^x}\\\\\bold{g(x)= (\frac{2}{3})^x}$

Following are the graph attachment to this question:

The second function, that is $g(x)= (\frac{2}{3})^x$ 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.

Answer 2

Answer:

The graphs are reflections of each other over the y-axis. The graph of g(x) shows exponential decay, while the graph of f(x) shows exponential growth.