Select The Correct Answer.Find The Value Of $h(-7)$ For The Function Below: $h(x) = 5.7 - 19x$.A. 0.67 B. -138.7 C. -127.3 D. 138.7

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Introduction

Functions are a fundamental concept in mathematics, and evaluating them is a crucial skill to master. In this article, we will focus on evaluating a specific function, h(x), and finding the value of h(-7). We will break down the process step by step, using the given function h(x) = 5.7 - 19x as an example.

Understanding the Function

Before we can evaluate the function, we need to understand its structure. The function h(x) is defined as:

h(x) = 5.7 - 19x

This function takes a single input, x, and returns a value based on the given expression. The expression consists of two terms: a constant term (5.7) and a variable term (-19x).

Evaluating the Function

To evaluate the function h(x) at x = -7, we need to substitute -7 into the function in place of x. This means we will replace every instance of x with -7.

h(-7) = 5.7 - 19(-7)

Order of Operations

When evaluating expressions, it's essential to follow the order of operations (PEMDAS):

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

Applying the Order of Operations

Now that we have the expression h(-7) = 5.7 - 19(-7), we can apply the order of operations:

  1. Evaluate the expression inside the parentheses: -19(-7) = 19(7) = 133
  2. Rewrite the expression: h(-7) = 5.7 - 133
  3. Subtract 133 from 5.7: h(-7) = -127.3

Conclusion

In this article, we evaluated the function h(x) = 5.7 - 19x at x = -7. We followed the order of operations and substituted -7 into the function in place of x. The result is h(-7) = -127.3.

Answer

The correct answer is:

  • C. -127.3

Discussion

Do you have any questions about evaluating functions or the order of operations? Share your thoughts and comments below!

Related Topics

  • Evaluating linear functions
  • Understanding the order of operations
  • Solving algebraic expressions

Additional Resources

  • Khan Academy: Evaluating functions
  • Mathway: Evaluating linear functions
  • Wolfram Alpha: Order of operations
    Evaluating Functions: A Q&A Guide =====================================

Introduction

In our previous article, we explored the concept of evaluating functions and applied it to a specific function, h(x) = 5.7 - 19x. We found the value of h(-7) to be -127.3. In this article, we will address some common questions and concerns related to evaluating functions.

Q&A

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS is commonly used to remember the order:

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

Q: How do I evaluate a function with multiple variables?

A: When evaluating a function with multiple variables, you need to substitute the given values into the function in place of the variables. For example, if you have a function f(x, y) = 2x + 3y and you want to evaluate it at x = 4 and y = 5, you would substitute 4 for x and 5 for y:

f(4, 5) = 2(4) + 3(5) = 8 + 15 = 23

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

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). It is often represented as a mathematical expression, such as f(x) = 2x + 3. An equation, on the other hand, is a statement that two expressions are equal, such as 2x + 3 = 5.

Q: How do I determine if a function is linear or non-linear?

A: A linear function is one that can be written in the form f(x) = mx + b, where m and b are constants. If a function cannot be written in this form, it is considered non-linear. For example, the function f(x) = 2x^2 + 3x is non-linear because it contains a quadratic term (x^2).

Q: What is the significance of the domain and range of a function?

A: The domain of a function is the set of all possible input values, while the range is the set of all possible output values. Understanding the domain and range of a function is crucial in evaluating its behavior and making predictions about its output.

Conclusion

Evaluating functions is a fundamental concept in mathematics, and understanding the order of operations, function notation, and domain and range is essential in applying it to real-world problems. We hope this Q&A guide has provided you with a better understanding of evaluating functions and has addressed some common questions and concerns.

Related Topics

  • Evaluating linear functions
  • Understanding the order of operations
  • Solving algebraic expressions
  • Domain and range of a function

Additional Resources

  • Khan Academy: Evaluating functions
  • Mathway: Evaluating linear functions
  • Wolfram Alpha: Order of operations
  • MIT OpenCourseWare: Functions and Graphs