Part 3/5:
Case 1: ( 0 < a < 1 )
When ( a ) is a fraction (e.g., ( \frac{1}{2} )), the graph of the function will decrease as ( x ) increases.
At ( x = 0 ), ( f(x) = 1 ).
As ( x ) approaches positive infinity, the graph decreases towards zero but never actually touches it.
Case 2: ( a = 1 )
In this case, the function simplifies to ( f(x) = 1^x = 1 ), forming a horizontal line at ( y = 1 ) across all values of ( x ).
Case 3: ( a > 1 )
For any value of ( a ) greater than one (e.g., 2), the graph will show an increasing trend:
At ( x = 0 ), the function will again yield ( f(x) = 1 ).
As ( x ) approaches positive infinity, ( f(x) ) goes to infinity while it approaches zero as ( x ) moves towards negative infinity.