Given The Function $g(x)=2x-8$, Evaluate Each Of The Following:For A, B, And C, Give The Exact Answer. For D And E, Give The Answer As A Simplified Expression.$\[ \begin{array}{|ll|} \hline \text{A) Evaluate } G(0) & G(0) = \square
Evaluating the Function g(x) = 2x - 8
Understanding the Function
The given function is g(x) = 2x - 8, where x is the input variable and g(x) is the output. This is a linear function, meaning it has a constant rate of change. To evaluate the function at a specific value of x, we simply substitute the value of x into the function and perform the necessary calculations.
Evaluating g(0)
To evaluate g(0), we substitute x = 0 into the function g(x) = 2x - 8.
g(0) = 2(0) - 8 g(0) = 0 - 8 g(0) = -8
Therefore, the exact answer for g(0) is -8.
Evaluating g(3)
To evaluate g(3), we substitute x = 3 into the function g(x) = 2x - 8.
g(3) = 2(3) - 8 g(3) = 6 - 8 g(3) = -2
Therefore, the exact answer for g(3) is -2.
Evaluating g(-2)
To evaluate g(-2), we substitute x = -2 into the function g(x) = 2x - 8.
g(-2) = 2(-2) - 8 g(-2) = -4 - 8 g(-2) = -12
Therefore, the exact answer for g(-2) is -12.
Evaluating g(x + 2)
To evaluate g(x + 2), we substitute x + 2 into the function g(x) = 2x - 8.
g(x + 2) = 2(x + 2) - 8 g(x + 2) = 2x + 4 - 8 g(x + 2) = 2x - 4
Therefore, the simplified expression for g(x + 2) is 2x - 4.
Evaluating g(2x)
To evaluate g(2x), we substitute 2x into the function g(x) = 2x - 8.
g(2x) = 2(2x) - 8 g(2x) = 4x - 8
Therefore, the simplified expression for g(2x) is 4x - 8.
Conclusion
In this article, we evaluated the function g(x) = 2x - 8 at various values of x. We found that the exact answers for g(0), g(3), and g(-2) are -8, -2, and -12, respectively. We also found that the simplified expressions for g(x + 2) and g(2x) are 2x - 4 and 4x - 8, respectively. These results demonstrate the importance of understanding and applying function notation in mathematics.
Key Takeaways
- The function g(x) = 2x - 8 is a linear function with a constant rate of change.
- To evaluate the function at a specific value of x, we substitute the value of x into the function and perform the necessary calculations.
- The exact answers for g(0), g(3), and g(-2) are -8, -2, and -12, respectively.
- The simplified expressions for g(x + 2) and g(2x) are 2x - 4 and 4x - 8, respectively.
Further Reading
For more information on function notation and linear functions, see the following resources:
References
- [1] "Function Notation" by Wikipedia. Retrieved February 2023.
- [2] "Linear Functions" by Wikipedia. Retrieved February 2023.
- [3] "Mathematics" by Wikipedia. Retrieved February 2023.
Evaluating the Function g(x) = 2x - 8: Q&A
Understanding the Function
The function g(x) = 2x - 8 is a linear function, meaning it has a constant rate of change. To evaluate the function at a specific value of x, we simply substitute the value of x into the function and perform the necessary calculations.
Q: What is the value of g(0)?
A: To evaluate g(0), we substitute x = 0 into the function g(x) = 2x - 8.
g(0) = 2(0) - 8 g(0) = 0 - 8 g(0) = -8
Therefore, the exact answer for g(0) is -8.
Q: What is the value of g(3)?
A: To evaluate g(3), we substitute x = 3 into the function g(x) = 2x - 8.
g(3) = 2(3) - 8 g(3) = 6 - 8 g(3) = -2
Therefore, the exact answer for g(3) is -2.
Q: What is the value of g(-2)?
A: To evaluate g(-2), we substitute x = -2 into the function g(x) = 2x - 8.
g(-2) = 2(-2) - 8 g(-2) = -4 - 8 g(-2) = -12
Therefore, the exact answer for g(-2) is -12.
Q: What is the simplified expression for g(x + 2)?
A: To evaluate g(x + 2), we substitute x + 2 into the function g(x) = 2x - 8.
g(x + 2) = 2(x + 2) - 8 g(x + 2) = 2x + 4 - 8 g(x + 2) = 2x - 4
Therefore, the simplified expression for g(x + 2) is 2x - 4.
Q: What is the simplified expression for g(2x)?
A: To evaluate g(2x), we substitute 2x into the function g(x) = 2x - 8.
g(2x) = 2(2x) - 8 g(2x) = 4x - 8
Therefore, the simplified expression for g(2x) is 4x - 8.
Q: How do I evaluate the function g(x) = 2x - 8 at a specific value of x?
A: To evaluate the function at a specific value of x, we simply substitute the value of x into the function and perform the necessary calculations.
Q: What is the importance of understanding and applying function notation in mathematics?
A: Understanding and applying function notation is crucial in mathematics as it allows us to represent and evaluate functions in a clear and concise manner. It also enables us to perform calculations and solve problems involving functions.
Q: What are some common applications of linear functions in real-life situations?
A: Linear functions have numerous applications in real-life situations, including:
- Modeling population growth and decline
- Representing the cost of goods and services
- Calculating the area and perimeter of shapes
- Determining the distance and time traveled by an object
Conclusion
In this article, we answered some common questions related to the function g(x) = 2x - 8. We evaluated the function at various values of x, found the simplified expressions for g(x + 2) and g(2x), and discussed the importance of understanding and applying function notation in mathematics. We also highlighted some common applications of linear functions in real-life situations.
Key Takeaways
- The function g(x) = 2x - 8 is a linear function with a constant rate of change.
- To evaluate the function at a specific value of x, we substitute the value of x into the function and perform the necessary calculations.
- The exact answers for g(0), g(3), and g(-2) are -8, -2, and -12, respectively.
- The simplified expressions for g(x + 2) and g(2x) are 2x - 4 and 4x - 8, respectively.
Further Reading
For more information on function notation and linear functions, see the following resources:
References
- [1] "Function Notation" by Wikipedia. Retrieved February 2023.
- [2] "Linear Functions" by Wikipedia. Retrieved February 2023.
- [3] "Mathematics" by Wikipedia. Retrieved February 2023.