Identify the following features of the graph of g(x) = (3/2)^x+2

A) Asymptotes
B) Intercepts
C) Increasing or decreasing

I really do not know how to find these

To identify the features of the graph of the function g(x) = (3/2)^(x+2), we can follow these steps:

Step 1: Understanding the Function Form
The given function is in the form of an exponential function, g(x) = a^(bx+c), where a is the base, b is the coefficient of x, and c is a constant term.

In this case, a = 3/2, b = 1, and c = 2. These values will help us determine the specific features of the graph.

A) Asymptotes:
To find the asymptotes (horizontal or vertical lines that the graph approaches but never touches), we need to evaluate the limits as x approaches positive or negative infinity.

Since the base (a) is greater than 1, the graph will have a horizontal asymptote at y = 0, or the x-axis.

B) Intercepts:
To find the x-intercepts, we set g(x) = 0 and solve for x:

0 = (3/2)^(x+2)

Since any number raised to the power of 0 is 1, this equation implies that there are no x-intercepts for this function.

To find the y-intercept, we set x = 0:

g(0) = (3/2)^(0+2) = (3/2)^2 = 9/4

So, the y-intercept is (0, 9/4) or (0, 2.25).

C) Increasing or Decreasing:
To determine whether g(x) is increasing or decreasing, we need to look at the sign of the coefficient b. If b is positive, the function is increasing; if b is negative, the function is decreasing.

In this case, b = 1, which is positive. Therefore, the function g(x) = (3/2)^(x+2) is increasing.

In summary, the features of the graph of g(x) = (3/2)^(x+2) are:
A) Horizontal asymptote at y = 0 (the x-axis)
B) No x-intercepts, y-intercept at (0, 2.25)
C) Increasing function.