What Is The Range Of The Function Y = 4 X − 7 Y = 4x - 7 Y = 4 X − 7 When The Domain Is { − 2 , − 1 , 3 } \{-2, -1, 3\} { − 2 , − 1 , 3 } ?

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Introduction

In mathematics, the range of a function is the set of all possible output values it can produce for the given input values. In other words, it is the set of all possible y-values that the function can take when the x-values are within the given domain. In this article, we will explore the range of the function y=4x−7y = 4x - 7 when the domain is {−2,−1,3}\{-2, -1, 3\}.

Understanding the Function

The given function is a linear function in the form of y=mx+by = mx + b, where mm is the slope and bb is the y-intercept. In this case, the slope is 44 and the y-intercept is −7-7. This means that for every unit increase in the x-value, the y-value increases by 44 units. The y-intercept is the point where the function intersects the y-axis, which is at (−7,0)(-7, 0).

Finding the Range

To find the range of the function, we need to substitute the given domain values into the function and calculate the corresponding y-values. The domain values are {−2,−1,3}\{-2, -1, 3\}, so we will substitute each of these values into the function and calculate the resulting y-values.

Substituting x=−2x = -2

When x=−2x = -2, the function becomes:

y=4(−2)−7y = 4(-2) - 7 y=−8−7y = -8 - 7 y=−15y = -15

So, when x=−2x = -2, the corresponding y-value is −15-15.

Substituting x=−1x = -1

When x=−1x = -1, the function becomes:

y=4(−1)−7y = 4(-1) - 7 y=−4−7y = -4 - 7 y=−11y = -11

So, when x=−1x = -1, the corresponding y-value is −11-11.

Substituting x=3x = 3

When x=3x = 3, the function becomes:

y=4(3)−7y = 4(3) - 7 y=12−7y = 12 - 7 y=5y = 5

So, when x=3x = 3, the corresponding y-value is 55.

Analyzing the Results

Now that we have calculated the y-values for each of the given domain values, we can analyze the results to determine the range of the function. The y-values we obtained are −15-15, −11-11, and 55. Since these values are all distinct, we can conclude that the range of the function is the set of all these values.

Conclusion

In conclusion, the range of the function y=4x−7y = 4x - 7 when the domain is {−2,−1,3}\{-2, -1, 3\} is {−15,−11,5}\{-15, -11, 5\}. This means that the function can produce any of these three values as output when the input values are within the given domain.

Final Thoughts

The range of a function is an important concept in mathematics, as it helps us understand the behavior of the function and its possible output values. In this article, we explored the range of the function y=4x−7y = 4x - 7 when the domain is {−2,−1,3}\{-2, -1, 3\}. We calculated the y-values for each of the given domain values and analyzed the results to determine the range of the function. We hope that this article has provided a clear understanding of the concept of range and how to find it for a given function.

Frequently Asked Questions

  • What is the range of a function? The range of a function is the set of all possible output values it can produce for the given input values.
  • How do I find the range of a function? To find the range of a function, you need to substitute the given domain values into the function and calculate the corresponding y-values.
  • What is the domain of a function? The domain of a function is the set of all possible input values it can accept.

References

Related Articles

  • [1] What is the Domain of the Function y=4x−7y = 4x - 7?
  • [2] How to Find the Range of a Function
  • [3] Understanding Linear Functions

Introduction

In our previous article, we explored the range of the function y=4x−7y = 4x - 7 when the domain is {−2,−1,3}\{-2, -1, 3\}. We calculated the y-values for each of the given domain values and analyzed the results to determine the range of the function. In this article, we will answer some frequently asked questions about the range of a function and provide additional insights into this important concept in mathematics.

Q&A

Q: What is the range of a function?

A: The range of a function is the set of all possible output values it can produce for the given input values.

Q: How do I find the range of a function?

A: To find the range of a function, you need to substitute the given domain values into the function and calculate the corresponding y-values.

Q: What is the domain of a function?

A: The domain of a function is the set of all possible input values it can accept.

Q: Can the range of a function be empty?

A: Yes, the range of a function can be empty if the function does not produce any output values for the given input values.

Q: Can the range of a function be infinite?

A: Yes, the range of a function can be infinite if the function produces an infinite number of output values for the given input values.

Q: How do I determine if the range of a function is finite or infinite?

A: To determine if the range of a function is finite or infinite, you need to analyze the function and its behavior. If the function produces a finite number of output values, then the range is finite. If the function produces an infinite number of output values, then the range is infinite.

Q: Can the range of a function be a single value?

A: Yes, the range of a function can be a single value if the function produces only one output value for the given input values.

Q: Can the range of a function be a set of values?

A: Yes, the range of a function can be a set of values if the function produces multiple output values for the given input values.

Q: How do I graph the range of a function?

A: To graph the range of a function, you need to plot the y-values on a coordinate plane. The resulting graph will show the range of the function.

Examples

Example 1: Finding the Range of a Function

Find the range of the function y=2x+1y = 2x + 1 when the domain is {0,1,2}\{0, 1, 2\}.

Solution:

  • Substitute the domain values into the function: y=2(0)+1=1y = 2(0) + 1 = 1, y=2(1)+1=3y = 2(1) + 1 = 3, y=2(2)+1=5y = 2(2) + 1 = 5
  • Analyze the results: The y-values are 11, 33, and 55, so the range of the function is {1,3,5}\{1, 3, 5\}.

Example 2: Determining the Range of a Function

Determine if the range of the function y=x2y = x^2 is finite or infinite.

Solution:

  • Analyze the function: The function y=x2y = x^2 produces an infinite number of output values for the given input values.
  • Conclusion: The range of the function y=x2y = x^2 is infinite.

Conclusion

In conclusion, the range of a function is an important concept in mathematics that helps us understand the behavior of the function and its possible output values. We have answered some frequently asked questions about the range of a function and provided additional insights into this concept. We hope that this article has provided a clear understanding of the range of a function and how to find it.

Final Thoughts

The range of a function is a fundamental concept in mathematics that has many applications in various fields, including science, engineering, and economics. Understanding the range of a function is essential for analyzing and solving problems in these fields. We hope that this article has provided a useful resource for students and professionals who want to learn more about the range of a function.

Frequently Asked Questions

  • What is the range of a function? The range of a function is the set of all possible output values it can produce for the given input values.
  • How do I find the range of a function? To find the range of a function, you need to substitute the given domain values into the function and calculate the corresponding y-values.
  • What is the domain of a function? The domain of a function is the set of all possible input values it can accept.

References

Related Articles

  • [1] What is the Domain of the Function y=4x−7y = 4x - 7?
  • [2] How to Find the Range of a Function
  • [3] Understanding Linear Functions