The Function $h$ Is Defined By $h(x)=3x+4$. Find \$h(a-4)$[/tex\]. $h(a-4)=$

Feb 26, 2025 by ADMIN 84 views

The Function h(x) and Its Applications in Mathematics

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Introduction

In mathematics, functions play a crucial role in representing relationships between variables. The function h(x) = 3x + 4 is a simple linear function that can be used to model various real-world scenarios. In this article, we will explore the function h(x) and its applications, particularly in finding the value of h(a-4).

Understanding the Function h(x)

The function h(x) = 3x + 4 is a linear function that takes an input value x and produces an output value h(x). The function has a slope of 3, which means that for every unit increase in x, h(x) increases by 3 units. The y-intercept of the function is 4, which means that when x is 0, h(x) is 4.

Finding h(a-4)

To find h(a-4), we need to substitute (a-4) into the function h(x) = 3x + 4. This means that we will replace x with (a-4) and simplify the expression.

Step 1: Substitute (a-4) into the Function

h(a-4) = 3(a-4) + 4

Step 2: Simplify the Expression

To simplify the expression, we need to distribute the 3 to the terms inside the parentheses.

h(a-4) = 3a - 12 + 4

Step 3: Combine Like Terms

Now, we can combine the like terms -12 and 4.

h(a-4) = 3a - 8

Conclusion

In conclusion, the value of h(a-4) is 3a - 8. This result can be used to model various real-world scenarios, such as the cost of a product that depends on the number of units produced.

Applications of the Function h(x)

The function h(x) = 3x + 4 has several applications in mathematics and real-world scenarios. Some of these applications include:

Cost-Volume-Profit Analysis

The function h(x) can be used to model the cost of a product that depends on the number of units produced. For example, if the cost of producing x units of a product is 3x + 4 dollars, then the cost of producing (a-4) units of the product is h(a-4) = 3(a-4) + 4 dollars.

Revenue and Profit Analysis

The function h(x) can also be used to model the revenue and profit of a business. For example, if the revenue from selling x units of a product is 3x + 4 dollars, then the revenue from selling (a-4) units of the product is h(a-4) = 3(a-4) + 4 dollars.

Real-World Applications

The function h(x) = 3x + 4 has several real-world applications, including:

Business and Finance

The function h(x) can be used to model the cost of a product, the revenue from selling a product, and the profit of a business.

Science and Engineering

The function h(x) can be used to model the relationship between variables in scientific and engineering applications, such as the cost of producing a product, the revenue from selling a product, and the profit of a business.

Conclusion

In conclusion, the function h(x) = 3x + 4 is a simple linear function that can be used to model various real-world scenarios. The value of h(a-4) is 3a - 8, and this result can be used to model the cost of a product that depends on the number of units produced. The function h(x) has several applications in mathematics and real-world scenarios, including cost-volume-profit analysis, revenue and profit analysis, and real-world applications in business and finance, science and engineering.

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Q&A

Q: What is the function h(x) = 3x + 4?

A: The function h(x) = 3x + 4 is a simple linear function that takes an input value x and produces an output value h(x). The function has a slope of 3, which means that for every unit increase in x, h(x) increases by 3 units. The y-intercept of the function is 4, which means that when x is 0, h(x) is 4.

Q: How do I find the value of h(a-4)?

A: To find the value of h(a-4), you need to substitute (a-4) into the function h(x) = 3x + 4. This means that you will replace x with (a-4) and simplify the expression.

Q: What is the value of h(a-4)?

A: The value of h(a-4) is 3a - 8.

Q: What are some real-world applications of the function h(x)?

A: The function h(x) = 3x + 4 has several real-world applications, including:

Cost-volume-profit analysis: The function can be used to model the cost of a product that depends on the number of units produced.
Revenue and profit analysis: The function can be used to model the revenue from selling a product and the profit of a business.
Business and finance: The function can be used to model the cost of a product, the revenue from selling a product, and the profit of a business.
Science and engineering: The function can be used to model the relationship between variables in scientific and engineering applications.

Q: How do I use the function h(x) in a real-world scenario?

A: To use the function h(x) in a real-world scenario, you need to identify the input value x and the output value h(x). For example, if you are modeling the cost of a product that depends on the number of units produced, you can use the function h(x) = 3x + 4 to calculate the cost of producing x units of the product.

Q: What are some common mistakes to avoid when using the function h(x)?

A: Some common mistakes to avoid when using the function h(x) include:

Not substituting the correct input value x into the function.
Not simplifying the expression correctly.
Not using the correct units of measurement.
Not considering the limitations of the function.

Q: How do I graph the function h(x)?

A: To graph the function h(x) = 3x + 4, you can use a graphing calculator or a computer program. You can also use a coordinate plane to plot the points (x, h(x)) and draw a line through the points.

Q: What are some common applications of the function h(x) in mathematics?

A: Some common applications of the function h(x) in mathematics include:

Algebra: The function can be used to model linear relationships between variables.
Calculus: The function can be used to model the derivative and integral of a function.
Statistics: The function can be used to model the mean and standard deviation of a dataset.