How to Evaluate a Function: Step-by-Step Guide for Students
Quick Answer
To evaluate the function f(x) = x² + 4x + 8 for f(-1), substitute -1 for x, resulting in f(-1) = 5. Your selected answer of 3 is incorrect.
Evaluating functions is a fundamental skill in mathematics, especially in algebra. It involves substituting a specific value for the variable in a function and simplifying the expression accordingly. In this guide, we'll walk through the process of evaluating the function f(x) = x² + 4x + 8 at x = -1.
To find f(-1), we begin by substituting -1 into the function where we see x:
**Step 1: Substitute**
- f(-1) = (-1)² + 4(-1) + 8
**Step 2: Calculate each part**
- First, compute (-1)². The square of -1 is 1.
- Next, calculate 4 times -1, which gives us -4.
- Finally, we have the constant term +8.
Putting it all together, we now have:
- f(-1) = 1 - 4 + 8
**Step 3: Simplify**
- Combine the numbers step-by-step:
- Start with 1 - 4, which equals -3.
- Then add 8 to -3, resulting in 5.
Thus, we find that f(-1) equals 5, making the correct answer 5, rather than the incorrect answer of 3 that was initially selected.
This type of error often arises from rushing through arithmetic steps. To avoid mistakes, take your time and ensure each calculation is accurate.
**Real-World Applications**
Understanding how to evaluate functions is crucial, as this skill is used in various real-world contexts, such as calculating distances, determining costs, or predicting outcomes based on variable inputs. For example, if you were to model the trajectory of a ball thrown into the air, the height of the ball at any given time could be described by a quadratic function similar to the one we evaluated here.
**Practice Makes Perfect**
If you’re interested in mastering this skill, consider practicing with additional substitution problems. The more you work with functions, the more intuitive it will become to evaluate them accurately. Check resources or worksheets available in the equations section for further practice.
By honing your function evaluation skills, you will build a solid foundation for more advanced topics in algebra and calculus. Keep practicing, and soon this process will become second nature!
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