An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Analyze the given table for function g ( x ) .
Evaluate each statement based on the table and general function knowledge.
Determine that statement 5 is false because g ( 2 ) is undefined.
A definitive answer for statements 1-4 requires information about function f .
Explanation
Problem Analysis We are given a table for a function g ( x ) and asked to evaluate five statements, selecting the correct ones. The key here is to analyze each statement based on the information we have about g ( x ) and general knowledge about functions.
Statement Analysis Let's analyze each statement:
'As x increases, f reaches a value of 4 earlier than g .' From the table, g ( 3 ) = 4 . This statement would be true if f ( x ) = 4 for some x < 3 . We don't have any information about f , so we cannot determine if this statement is true or false.
'As x increases, g reaches a value of 4 earlier than f .' From the table, g ( 3 ) = 4 . This statement would be true if f ( x ) = 4 for some 3"> x > 3 or if f ( x ) never equals 4. We don't have any information about f , so we cannot determine if this statement is true or false.
'The vertical asymptote of f is to the left of the vertical asymptote of g .' From the table, g ( 2 ) is undefined, suggesting a vertical asymptote at x = 2 for g . This statement would be true if f has a vertical asymptote at some x < 2 . We don't have any information about f , so we cannot determine if this statement is true or false.
'The vertical asymptote of g is to the left of the vertical asymptote of f .' From the table, g ( 2 ) is undefined, suggesting a vertical asymptote at x = 2 for g . This statement would be true if f has a vertical asymptote at some 2"> x > 2 . We don't have any information about f , so we cannot determine if this statement is true or false.
'Both f and g pass through the point ( 2 , 4 ) .' From the table, g ( 2 ) is undefined, so g does not pass through ( 2 , 4 ) . Therefore, this statement is false.
Further Considerations Since we cannot definitively determine the truth of the first four statements without more information about the function f , and we know the fifth statement is false, we can only conclude that the fifth statement is incorrect. However, we can analyze the statements assuming different scenarios for f ( x ) .
Examples
Understanding functions and their properties, such as asymptotes and specific values, is crucial in many real-world applications. For example, in physics, understanding the behavior of functions that model radioactive decay or the motion of objects can help predict future states. In economics, functions are used to model supply and demand curves, and understanding their asymptotes and key values can help predict market behavior. In computer science, functions are used to model algorithms, and understanding their properties can help optimize performance.
