Math Problem Statement
Based on the table, what is the correct expression for h(x)?
Solution
The problem presents two tables, one for and another for , and asks you to find a relationship between the two, specifically which of the given options defines in terms of .
Table for :
\hline x & -2 & -1 & 0 & 1 & 2 \\ \hline f(x) & -3 & 1 & 2 & 3 & -2 \\ \hline \end{array}$$ ### Table for $$h(x)$$: $$\begin{array}{|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 \\ \hline h(x) & -4 & 0 & 1 & 2 & -3 \\ \hline \end{array}$$ We need to analyze how $$h(x)$$ is related to $$f(x)$$. Let's compare the values of $$h(x)$$ and $$f(x)$$ directly: - For $$x = -2$$: $$f(-2) = -3$$, $$h(-2) = -4$$ → $$h(-2) = f(-2) - 1$$ - For $$x = -1$$: $$f(-1) = 1$$, $$h(-1) = 0$$ → $$h(-1) = f(-1) - 1$$ - For $$x = 0$$: $$f(0) = 2$$, $$h(0) = 1$$ → $$h(0) = f(0) - 1$$ - For $$x = 1$$: $$f(1) = 3$$, $$h(1) = 2$$ → $$h(1) = f(1) - 1$$ - For $$x = 2$$: $$f(2) = -2$$, $$h(2) = -3$$ → $$h(2) = f(2) - 1$$ It appears that the values of $$h(x)$$ are always 1 less than $$f(x)$$. ### Conclusion: The correct relationship is: $$h(x) = f(x) - 1$$ So, the correct answer is **$$h(x) = f(x) - 1$$**. Would you like further details or clarification? Here are five related questions to expand your understanding: 1. How do function transformations generally affect a function? 2. What is the significance of vertical shifts in function transformations? 3. How would $$h(x) = f(x) + 2$$ affect the graph of $$f(x)$$? 4. Can you provide examples of horizontal shifts and their effects on functions? 5. How would you express $$h(x)$$ if it were shifted by 2 units downward? **Tip:** When analyzing tables for functions, look for consistent differences between corresponding values to identify transformations like shifts, stretches, or reflections.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Function transformations
Algebra
Formulas
h(x) = f(x) - 1
Theorems
Vertical shift of functions
Suitable Grade Level
Grades 8-10
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