Short Answer 
The functions analyzed are exponential and can be represented as y = ab^x, with ‘a’ as the y-intercept and ‘b’ determining the graph’s behavior. If ‘b’ is less than 1, the graph approaches 0; if greater than 1, it approaches positive infinity. Specific examples show the y-intercepts and behaviors for each function.
Step 1: Identify the Function Form
Understand that the given functions are all in the form of exponential functions, which are expressed as y = abx. In this representation, ‘a’ denotes the y-intercept, and ‘b’ indicates the base of the exponential. Knowing this will help you to analyze the properties correctly based on the values of ‘a’ and ‘b’.
Step 2: Analyze the Value of ‘b’
Examine the value of ‘b’ in each function to determine the behavior of the graph. If b is less than 1, the graph will approach 0 as x increases. Conversely, if b is greater than 1, the graph will approach positive infinity. This characteristic is crucial for matching each function with its graphical behavior.
- y = (1/4)‚à öa¬¨¬£: b = 1/4 (less than 1, approaches 0)
- y = 2(1/2)‚à öa¬¨¬£: b = 1/2 (less than 1, approaches 0)
- y = 3‚à öa¬¨¬£: b = 3 (greater than 1, approaches positive infinity)
Step 3: Plot the Properties According to Their Y-Intercepts
Match each function with its corresponding properties based on their y-intercepts and end behavior. The y-intercept is derived from the value of ‘a’ in each equation, which indicates where the graph crosses the y-axis. Compile your findings into a list of properties as follows:
- y = (1/4)‚à öa¬¨¬£: y-intercept at (0,1), approaches 0
- y = 2(1/2)‚à öa¬¨¬£: y-intercept at (0,2), approaches 0
- y = 3‚à öa¬¨¬£: y-intercept at (0,3), approaches positive infinity