Understanding Linear Functions: Finding Maximum Outputs
Quick Answer
In the linear function f(x) = 3 - 2x, the output decreases as x increases. Thus, the maximum output occurs at the smallest x-value, which is f(0) = 3.
When working with linear functions, it's crucial to understand how the variables interact. The function f(x) = 3 - 2x is a perfect example of this interaction. Here, the output of the function, represented as f(x), changes based on the value of x you input.
To analyze this function, look closely at its components. The term '-2x' indicates that as x increases, the overall value of f(x) decreases. This is because you're subtracting a larger number as x gets bigger. Therefore, if you're trying to find the highest output of this function, you should consider smaller values of x.
Let’s evaluate some specific values to see how this works:
- When x = 0: f(0) = 3 - 2*0 = 3 - 0 = 3
- When x = 2: f(2) = 3 - 2*2 = 3 - 4 = -1
- When x = 3: f(3) = 3 - 2*3 = 3 - 6 = -3
- When x = 5: f(5) = 3 - 2*5 = 3 - 10 = -7
From these calculations, it's clear that the function outputs the highest value when x is at its smallest, in this case, 0. The maximum output of f(x) is 3 when x is 0, showcasing how linear functions can behave in a downward trend as the input values increase.
Understanding these principles can be very helpful in various real-world scenarios. For instance, in economics, such functions can model cost and revenue where you want to maximize profit (the output) based on certain constraints (the inputs). This concept also appears in physics, where you might analyze speed over time or other changing variables.
In conclusion, remember that for functions like f(x) = 3 - 2x, the highest output corresponds to the smallest input. So when analyzing linear functions, always consider how the coefficients affect the overall behavior of the function. For more detailed guidance, check the equations section where all steps are outlined clearly.
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