How to Evaluate Functions: Finding f(-2) for f(x) = 4x² - 3x + 7
Quick Answer
To evaluate the function f(x) = 4x² - 3x + 7 at x = -2, plug in -2 for x. This leads to f(-2) = 4(-2)² - 3(-2) + 7, which simplifies to 35.
Evaluating functions is a fundamental skill in mathematics. Let's take the function f(x) = 4x² - 3x + 7 and find its value at x = -2. This process is often referred to as 'plugging in' the value of x into the function.
The first step is to replace every instance of x in the function with -2. This means we will write:
f(-2) = 4(-2)² - 3(-2) + 7.
Now, let's break this down step by step.
1. **Calculating (-2)²:** The first operation we need to perform is to square -2. Remember, squaring a number means multiplying it by itself. So, (-2)² = (-2) × (-2) = 4.
2. **Substituting back into the function:** Now, we substitute this result back into our equation:
f(-2) = 4(4) - 3(-2) + 7.
3. **Multiplying by 4:** Next, we multiply 4 by 4, which gives us 16:
f(-2) = 16 - 3(-2) + 7.
4. **Calculating -3(-2):** Now, we need to deal with -3(-2). When you multiply a negative number by a negative number, the result is positive, so -3(-2) = 6.
5. **Final substitution:** Replacing -3(-2) in our equation gives:
f(-2) = 16 + 6 + 7.
6. **Adding it all up:** Finally, we add these values together: 16 + 6 + 7 = 29.
So, the value of f(-2) is 29.
Understanding how to evaluate functions by substituting values is not only important for solving equations in algebra but also for real-world applications. For example, if f(x) represents the profit function of a business based on the number of items sold, finding f(-2) might help analyze what happens when fewer items are sold, albeit in a theoretical or abstract manner since negative sales don't usually apply in real life.
By practicing these steps, you can confidently evaluate any function at different points. Keep working through examples, and soon this method will become second nature!
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