Select The Correct Answer.Find The Value Of $g(25)$ For The Function Below.$g(x) = 24(x - 39)$A. -911 B. -14 C. 561 D. -336

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Understanding the Function g(x)

The given function is g(x) = 24(x - 39). To find the value of g(25), we need to substitute x = 25 into the function and evaluate the expression.

Substituting x = 25 into the Function

To find the value of g(25), we will replace x with 25 in the function g(x) = 24(x - 39).

g(25) = 24(25 - 39)

Evaluating the Expression

Now, we need to evaluate the expression inside the parentheses first. Subtracting 39 from 25 gives us:

25 - 39 = -14

Multiplying by 24

Next, we multiply the result by 24:

24(-14) = -336

Conclusion

Therefore, the value of g(25) for the function g(x) = 24(x - 39) is -336.

Comparing the Answer with the Options

Comparing our result with the given options, we can see that the correct answer is:

  • D. -336

Why the Other Options are Incorrect

Let's quickly evaluate the other options to see why they are incorrect:

  • A. -911: This is not the correct result of the function g(x) = 24(x - 39) when x = 25.
  • B. -14: This is the result of subtracting 39 from 25, but we need to multiply it by 24 to get the final result.
  • C. 561: This is not the correct result of the function g(x) = 24(x - 39) when x = 25.

Key Takeaways

  • To evaluate a function at a specific value, we need to substitute the value into the function and evaluate the expression.
  • When evaluating expressions, we need to follow the order of operations (PEMDAS): parentheses, exponents, multiplication and division, and addition and subtraction.
  • In this case, we need to subtract 39 from 25 and then multiply the result by 24 to get the final result.

Real-World Applications

Evaluating functions is a fundamental concept in mathematics that has many real-world applications. For example, in physics, we use functions to describe the motion of objects and to calculate quantities such as velocity and acceleration. In economics, we use functions to model the behavior of markets and to make predictions about future trends.

Common Mistakes to Avoid

When evaluating functions, some common mistakes to avoid include:

  • Not following the order of operations (PEMDAS)
  • Not substituting the correct value into the function
  • Not evaluating the expression correctly

Conclusion

In conclusion, evaluating the function g(x) = 24(x - 39) at x = 25 gives us a value of -336. This is the correct answer among the given options. We hope this explanation has helped you understand how to evaluate functions and has provided you with a clear understanding of the concept.

Understanding Functions

A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). It is a way of describing a relationship between variables. In the context of the previous article, we evaluated the function g(x) = 24(x - 39) at x = 25.

Q&A: Evaluating Functions

Q: What is the difference between a function and an equation?

A: A function is a relation between a set of inputs and a set of possible outputs, whereas an equation is a statement that two expressions are equal. For example, the equation x + 2 = 5 is not a function, but the expression f(x) = x + 2 is a function.

Q: How do I evaluate a function at a specific value?

A: To evaluate a function at a specific value, you need to substitute the value into the function and evaluate the expression. For example, to evaluate the function g(x) = 24(x - 39) at x = 25, you would substitute 25 into the function and evaluate the expression.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when evaluating an expression. The acronym PEMDAS stands for:

  • Parentheses: Evaluate expressions inside parentheses first.
  • Exponents: Evaluate any exponential expressions next.
  • Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  • Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between a function and a relation?

A: A function is a relation between a set of inputs and a set of possible outputs, where each input corresponds to exactly one output. A relation, on the other hand, is a set of ordered pairs, where each pair represents a possible input-output combination. For example, the relation {(1, 2), (2, 3), (3, 4)} is not a function, because the input 2 corresponds to two different outputs (3 and 4).

Q: How do I determine if a relation is a function?

A: To determine if a relation is a function, you need to check if each input corresponds to exactly one output. If each input corresponds to exactly one output, then the relation is a function.

Q: What is the domain of a function?

A: The domain of a function is the set of all possible input values. For example, the domain of the function g(x) = 24(x - 39) is all real numbers.

Q: What is the range of a function?

A: The range of a function is the set of all possible output values. For example, the range of the function g(x) = 24(x - 39) is all real numbers.

Conclusion

In conclusion, evaluating functions is a fundamental concept in mathematics that has many real-world applications. We hope this Q&A guide has helped you understand how to evaluate functions and has provided you with a clear understanding of the concept.

Common Mistakes to Avoid

When evaluating functions, some common mistakes to avoid include:

  • Not following the order of operations (PEMDAS)
  • Not substituting the correct value into the function
  • Not evaluating the expression correctly
  • Not checking if a relation is a function

Real-World Applications

Evaluating functions is a fundamental concept in mathematics that has many real-world applications. For example, in physics, we use functions to describe the motion of objects and to calculate quantities such as velocity and acceleration. In economics, we use functions to model the behavior of markets and to make predictions about future trends.

Final Tips

  • Always follow the order of operations (PEMDAS) when evaluating expressions.
  • Make sure to substitute the correct value into the function.
  • Check if a relation is a function before using it.
  • Use functions to model real-world phenomena and make predictions about future trends.