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Understanding and Evaluating Mathematical Functions: fx x^2 - 2x for Given Values
Understanding and Evaluating Mathematical Functions: fx x^2 - 2x for Given Values
When working with mathematical functions, it's important to understand how to evaluate these expressions for specific values of the variable. In this article, we will evaluate the function fx x^2 - 2x for x -2 and provide a detailed step-by-step approach to solving it. We will also explore the importance of following the order of operations, commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).
Evaluating the Function for x -2
The given function is:
fx x^2 - 2x
Let#39;s substitute x -2 into the function and solve it step-by-step.
Substitute x -2 into the function: Calculate the expression step-by-step using the order of operations (PEMDAS).Step-by-Step Solution
Solution 1: Substitute x -2 into the function:f(-2) (-2)^2 - 2(-2)
Calculate the exponent first (Exponent: E in PEMDAS):f(-2) 4 - 2(-2)
Then, perform the multiplication (Multiplication/Multiplication: M in PEMDAS):f(-2) 4 - (-4) (since -2 * -2 4)
Next, perform the addition (Addition: A in PEMDAS):f(-2) 4 4 8
Therefore, the value of the function for x -2 is 8.Alternative Solution
Solution 2: Substitute x -2 into the function:f(-2) (-2)^2 - 2(-2)
Calculate the exponent first (Exponent: E in PEMDAS):f(-2) 4 - 2(-2)
Then, perform the multiplication (Multiplication/Multiplication: M in PEMDAS):f(-2) 4 - (-4) (since -2 * -2 4)
Next, perform the addition (Addition: A in PEMDAS):f(-2) 4 4 8
Therefore, the value of the function for x -2 is 8.The Importance of Order of Operations (PEMDAS)
Understanding the correct order of operations is crucial for accurately evaluating mathematical expressions. PEMDAS is a mnemonic to help remember the order:
Parentheses Exponents Multiplication and Division (from left to right) Addition and Subtraction (from left to right)Using the correct order ensures that we evaluate the function correctly. For instance, in the function 2x^2 - 2x with x -2:
First, calculate the exponent: 2(-2)^2 - 2(-2) Calculate (-2)^2 4. Then, perform the multiplication: 2(4) - 2(-2) Perform the multiplication: 8 4 Add the results: 8 4 12.The mistake in the provided solutions is in the handling of the exponent and the term -2(-2). The correct solution should be:
Substitute x -2 into the function:2(-2)^2 - 2(-2)
Calculate the exponent first: 2(4) - 2(-2) Perform the multiplication: 8 4 Add the results: 8 4 12.Conclusion
Evaluating mathematical functions for specific values of variables is a fundamental skill in algebra. By understanding and applying the correct order of operations, we can accurately calculate the value of functions. In this case, when evaluating fx x^2 - 2x for x -2, the correct value is 8. This understanding can be applied to a wide range of mathematical problems, making it an essential skill for students and professionals alike.