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

A) Asymptotes
B) Intercepts
C) Increasing or decreasing

Once I graph this on my calculator, how can I find these?

sounds like you are using a graphing calculator, I don't have one of those.

But I can visualize the graph,
since the base is (3/2) , as x ---> large +
g(x) becomes very large, so the curve rises to the right
as x ---> large - , we get 1/"large" -----> 0

the curve approaches the x-axis to the left, and there is a horizontal asymptote at y = 0

when x = -2 , y = 1, so the y-intercept is 1

To graph the function g(x) = (3/2)^(x+2) on your calculator, follow these steps:

1. Input the equation in the graphing calculator. Most graphing calculators have a specific button for entering exponential expressions.

2. Adjust the window settings. Make sure the window settings are appropriate to see the graph clearly. It is usually helpful to set a suitable range for the x-axis and y-axis.

3. Graph the equation. Once you have entered the equation and set the window settings, press the graph button to plot the graph on your calculator screen.

Now that you have the graph displayed on your calculator, you can determine the features of the graph:

A) Asymptotes: Look for any vertical or horizontal lines where the graph approaches but does not reach. Horizontal asymptotes occur when the value of the function approaches a specific value as x heads towards infinity or negative infinity. Vertical asymptotes occur when the function approaches infinity or negative infinity as x approaches a specific value.

To find any asymptotes on the graph, observe the behavior of the graph as x becomes very large or very small (positive or negative). If the graph approaches a specific value (horizontal asymptote) or tends towards infinity (vertical asymptote), note the corresponding equations of the asymptotes.

B) Intercepts: There are two types of intercepts to consider - x-intercepts (where the graph intersects the x-axis) and y-intercepts (where the graph intersects the y-axis).

To find x-intercepts, look for the points on the graph where y equals zero. These points will correspond to the values of x where the graph crosses the x-axis. You can use the "zero" or "solve" function on your calculator to find the x-intercepts.

To find the y-intercept, determine the value of y when x = 0. This point will correspond to the value where the graph intersects the y-axis.

C) Increasing or Decreasing: To determine where the function is increasing or decreasing, analyze the slope of the graph. If the graph is going uphill from left to right, it is increasing. If the graph is going downhill from left to right, it is decreasing.

You can determine the increasing or decreasing intervals by considering the sign of the first derivative of the function. However, if you want to identify the trend visually, observe the slope of the graph as it moves from left to right.