Math Problem Statement
GPT4
To make a table for h(x)=g(x−1)+5h(x)=g(x−1)+5 for values of x=1,2,3,4x=1,2,3,4, you'll need to follow these steps:
Solution
To make a table for the function for , follow these steps:
Steps:
-
Understand the function: The given function is . This means that for any value of , depends on the value of , with an additional constant term of 5.
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Define or obtain : The function must be defined or given to calculate . If the values of are known, substitute them into for each . Without specific information on , we can only express the results in terms of .
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Substitute values of : Now, substitute the values of into the formula to compute .
Substitution:
- For :
- For :
- For :
- For :
Table Structure:
1 | ||
2 | ||
3 | ||
4 |
Final Notes:
- You need to know the values of to complete the table. Without knowing , the result stays expressed in terms of .
Would you like to provide specific values for to fill in the table? Or would you like more details on any of the steps?
Here are 5 related questions you might explore:
- What happens if is a specific polynomial function, like ?
- How does the table change if includes other constants besides 5?
- What is the interpretation of in practical problems?
- How can we differentiate or integrate if is continuous?
- How do different transformations of affect the form of ?
Tip: Always clarify the domain and range of the function before working with composite functions like .
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Math Problem Analysis
Mathematical Concepts
Functions
Substitution
Table of Values
Formulas
h(x) = g(x-1) + 5
Theorems
Function Composition
Suitable Grade Level
Grades 9-12