How do the graphs of the functions f(x) = (3/2)^x and g(x) = (2/3)^x compare?

Solution:

Given, the function f(x) = (3/2)^x

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

We have to compare the graphs of the functions f(x) and g(x).

Exponential function is of the form: y = ab^x

Where a is the initial value and b is the growth factor.

a) If b > 1, then the function is an exponential growth function.

b) If 0 < b < 1, then the function is an exponential decay function.

f(x) = y = (3/2)^x

The function is an exponential growth function.

The rule of reflection over y-axis:

(x, y) → (-x, y)

Applying the rule, we get,

(3/2)^x = (3/2)^-x

= (2/3)^x

= g(x)

Therefore, the function g(x) = (2/3)ˣ is the graph of the function f(x) reflected over y-axis.

---

How do the graphs of the functions f(x) = (3/2)^x and g(x) = (2/3)^x compare?

Summary:

The function g(x) = (2/3)^x is the graph of the function f(x) = (3/2)^x reflected over y-axis.