Check the definition below. Present another real-life situation to explain the meaning of functions.
- The area [tex]$A$[/tex] of a circle depends on the radius [tex]$r$[/tex] of the circle. The rule that connects [tex]$r$[/tex] and [tex]$A$[/tex] is given by the equation [tex]$A=\pi r^2$[/tex]. With each positive number [tex]$r$[/tex] there is associated one value of [tex]$A$[/tex], and we say that [tex]$A$[/tex] is a function of [tex]$r$[/tex].
Answer (1)
The total cost C of buying apples is a function of the number of apples n purchased.
If each apple costs $0.75 , the relationship is expressed as C = 0.75 n .
For each number of apples n , there is exactly one total cost C , satisfying the definition of a function.
Therefore, the total cost is a function of the number of apples: C = 0.75 n .
Explanation
Understanding the Problem We are given the definition of a function using the example of the area of a circle depending on its radius. We need to provide another real-life example to illustrate the concept of a function.
Real-Life Example: Buying Apples Consider the relationship between the number of items purchased and the total cost. Suppose you are buying apples at a store where each apple costs a fixed price. The total cost C depends on the number of apples n you buy. If each apple costs $0.75 , the total cost is given by the equation C = 0.75 n .
Explanation of the Function In this scenario, the number of apples n is the input, and the total cost C is the output. For each number of apples you buy, there is exactly one total cost. For example, if you buy 1 apple, the total cost is $0.75 . If you buy 2 apples, the total cost is $1.50 . This relationship satisfies the definition of a function because each input (number of apples) is associated with exactly one output (total cost).
Another Example: Fuel Consumption Another example is the relationship between the distance traveled by a car and the amount of fuel consumed. The amount of fuel consumed, F , is a function of the distance traveled, d , given a fixed fuel consumption rate, r (e.g., miles per gallon). The equation is F = d / r .
Final Answer In conclusion, the relationship between the number of apples purchased and the total cost is a function because for each number of apples, there is a unique total cost. The total cost C is a function of the number of apples n , represented by the equation C = 0.75 n .
Examples
Understanding functions is crucial in everyday life. For instance, when planning a road trip, the amount of gas you need is a function of the distance you'll travel. If your car gets 30 miles per gallon, you can calculate the gallons needed for a 300-mile trip using the function g = d /30 , where g is gallons and d is distance. This helps you estimate costs and plan fuel stops, making functions a practical tool for efficient travel planning.
