What Is The Output Value Of The Given Function When The Input Value Is -6?$\[ \begin{array}{l} y = 3x + 14 \\ (-6, \; [?]) \end{array} \\]

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Introduction

In mathematics, functions are used to describe the relationship between two variables, typically denoted as input and output. The output value of a function is determined by the input value, and it is calculated using a specific formula or rule. In this article, we will explore the concept of functions and how to find the output value of a given function when the input value is known.

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 two variables, where each input value corresponds to a unique output value. The function is typically denoted as f(x), where x is the input value and f(x) is the output value.

The Given Function

The given function is y = 3x + 14, where x is the input value and y is the output value. This function is a linear function, which means that it has a constant rate of change between any two points on the graph. The slope of the function is 3, which means that for every unit increase in x, the value of y increases by 3 units.

Finding the Output Value

To find the output value of the given function when the input value is -6, we need to substitute x = -6 into the function and calculate the corresponding value of y. This can be done using the following steps:

  1. Substitute x = -6 into the function: y = 3(-6) + 14
  2. Simplify the expression: y = -18 + 14
  3. Calculate the final value: y = -4

Therefore, the output value of the given function when the input value is -6 is -4.

Graphical Representation

The graph of the given function is a straight line with a slope of 3 and a y-intercept of 14. The graph can be represented as follows:

y = 3x + 14

The graph passes through the point (0, 14), which is the y-intercept. The graph also passes through the point (-6, -4), which is the point corresponding to the input value x = -6.

Conclusion

In conclusion, the output value of the given function when the input value is -6 is -4. This can be calculated using the function y = 3x + 14 and substituting x = -6 into the function. The graph of the function is a straight line with a slope of 3 and a y-intercept of 14.

Frequently Asked Questions

  • What is the output value of the given function when the input value is -6? The output value of the given function when the input value is -6 is -4.
  • What is the slope of the given function? The slope of the given function is 3.
  • What is the y-intercept of the given function? The y-intercept of the given function is 14.

Final Thoughts

In this article, we have explored the concept of functions and how to find the output value of a given function when the input value is known. We have used the function y = 3x + 14 as an example and calculated the output value when the input value is -6. The graph of the function is a straight line with a slope of 3 and a y-intercept of 14. We hope that this article has provided a clear understanding of functions and how to calculate the output value of a given function.

Introduction

In our previous article, we explored the concept of functions and how to find the output value of a given function when the input value is known. In this article, we will answer some frequently asked questions about functions to provide a deeper understanding of this mathematical concept.

Q&A

Q1: What is a function?

A1: 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 two variables, where each input value corresponds to a unique output value.

Q2: What is the difference between a function and a relation?

A2: A function is a relation where each input value corresponds to a unique output value, whereas a relation is a set of ordered pairs where each input value may correspond to multiple output values.

Q3: What is the domain of a function?

A3: The domain of a function is the set of all possible input values for which the function is defined.

Q4: What is the range of a function?

A4: The range of a function is the set of all possible output values for which the function is defined.

Q5: What is the slope of a function?

A5: The slope of a function is a measure of how steep the function is at a given point. It is calculated as the ratio of the change in output value to the change in input value.

Q6: What is the y-intercept of a function?

A6: The y-intercept of a function is the point where the function intersects the y-axis. It is the value of the function when the input value is 0.

Q7: How do I find the output value of a function when the input value is known?

A7: To find the output value of a function when the input value is known, you need to substitute the input value into the function and calculate the corresponding output value.

Q8: What is the difference between a linear function and a non-linear function?

A8: A linear function is a function where the output value changes at a constant rate with respect to the input value, whereas a non-linear function is a function where the output value changes at a non-constant rate with respect to the input value.

Q9: How do I graph a function?

A9: To graph a function, you need to plot the points on the graph that correspond to the input and output values of the function. You can use a table of values or a graphing calculator to help you graph the function.

Q10: What is the importance of functions in mathematics?

A10: Functions are an essential concept in mathematics, as they provide a way to describe relationships between variables and to model real-world phenomena. They are used in a wide range of fields, including physics, engineering, economics, and computer science.

Conclusion

In conclusion, functions are a fundamental concept in mathematics that provide a way to describe relationships between variables and to model real-world phenomena. We hope that this article has provided a clear understanding of functions and how to answer some frequently asked questions about them.

Final Thoughts

Functions are a powerful tool in mathematics that can be used to solve a wide range of problems. By understanding the concept of functions and how to graph them, you can gain a deeper understanding of mathematical relationships and model real-world phenomena.

Additional Resources

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Tags

  • Functions
  • Graphing Functions
  • Linear Functions
  • Non-Linear Functions
  • Domain
  • Range
  • Slope
  • Y-Intercept
  • Input Value
  • Output Value