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 asymptotes, intercepts, and whether the function is increasing or decreasing, we need to understand the properties of the graph of the given function, g(x) = (3/2)^(x+2).

Before identifying these features, let's discuss the general properties of exponential functions. In an exponential function of the form f(x) = a^x, where "a" is a positive constant, the graph typically exhibits the following characteristics:

1) Asymptotes: Exponential functions do not have horizontal asymptotes. Instead, they have a vertical asymptote at x = -∞ (approaching negative infinity). This means that the graph gets infinitely close to the y-axis, but never touches it.

2) Intercepts: Exponential functions do not generally have x-intercepts (where the graph intersects the x-axis). However, they almost always have a y-intercept, which is the point where the graph intersects the y-axis (x = 0).

3) Increasing or Decreasing: The behavior of an exponential function depends on the value of the base, "a." If a > 1, the function is increasing, meaning it rises from left to right. If 0 < a < 1, the function is decreasing, meaning it declines from left to right.

Now, let's apply these properties to the given function, g(x) = (3/2)^(x+2), to answer each part of the question:

A) Asymptotes: Since the base, 3/2, is greater than 1, there is no horizontal asymptote. However, the vertical asymptote is x = -2. This means that the graph of g(x) approaches but never touches the line x = -2.

B) Intercepts: To find the y-intercept, substitute x = 0 into the function:
g(0) = (3/2)^(0+2) = (3/2)^2 = 9/4
So, the y-intercept is (0, 9/4).

C) Increasing or Decreasing: Since the base, 3/2, is greater than 1, the function g(x) = (3/2)^(x+2) is increasing. This means that as x increases, g(x) also increases.

In summary:
A) Asymptotes: Vertical asymptote at x = -2.
B) Intercepts: Y-intercept at (0, 9/4).
C) Increasing or Decreasing: Increasing.

Remember, the procedures described here can be applied to analyze the properties of most exponential functions.