Distance Traveled in a Car: Imagine you're driving a car and are interested in understanding how the distance you travel ( D ) is related to the time you spend driving ( t ). Let's say your car travels at a constant speed of 60 miles per hour. The relationship between distance ( D ) and time ( t ) in this scenario can be represented by a mathematical function: D(t) = 60t In this function: - D(t) represents the distance traveled at time t hours. - 60t is the speed of the car (60 miles per hour) multiplied by the time ( t ). This function describes the relationship: for any given time t , you can plug it into the function, and it will provide you with the distance traveled. Example: - If you drive for 1 hour ( t = 1 ), plug it into the function: D(1) = 60(1) = 60 So, after 1 hour of driving, you've traveled 60 miles. - If you drive for 2 hours ( t = 2 ), plug it into the function: D(2) = 60(2) = 120 After 2 hours, you've traveled 120 miles. This function represents the idea of a mathematical function: it takes an input ( t , the time), performs a specific operation on it (multiplying by 60), and gives a unique output ( D , the distance traveled) for each input. It's like a formula that tells you how far you'll travel based on how much time you drive at a constant speed.
