Math Problem Statement

H(x) is wrong

Solution

Let's carefully analyze h(x)h(x) again to determine the correct relationship with f(x)f(x).

Reanalysis for h(x)h(x):

The given table for f(x)f(x) is:

x & -2 & -1 & 0 & 1 & 2 \\ \hline f(x) & 1 & -4 & 4 & -3 & 2 \\ \end{array}$$ The table for $$h(x)$$ is: $$\begin{array}{c|c|c|c|c|c} x & -2 & -1 & 0 & 1 & 2 \\ \hline h(x) & 2 & -3 & 5 & -2 & 3 \\ \end{array}$$ We need to find how $$h(x)$$ relates to $$f(x)$$. ### Step-by-step Comparison: We check if $$h(x)$$ matches any of the given options: 1. **Option: $$h(x) = f(x) + 1$$** - For $$x = -2$$, $$f(-2) = 1$$, so $$f(-2) + 1 = 1 + 1 = 2$$, which matches $$h(-2) = 2$$. - For $$x = -1$$, $$f(-1) = -4$$, so $$f(-1) + 1 = -4 + 1 = -3$$, which matches $$h(-1) = -3$$. - For $$x = 0$$, $$f(0) = 4$$, so $$f(0) + 1 = 4 + 1 = 5$$, which matches $$h(0) = 5$$. - For $$x = 1$$, $$f(1) = -3$$, so $$f(1) + 1 = -3 + 1 = -2$$, which matches $$h(1) = -2$$. - For $$x = 2$$, $$f(2) = 2$$, so $$f(2) + 1 = 2 + 1 = 3$$, which matches $$h(2) = 3$$. All values match perfectly, so the correct answer is: $$\boxed{h(x) = f(x) + 1}$$ Thank you for catching that mistake. Would you like more details or have any other questions? ### Related Questions to Explore: 1. What is the difference between horizontal and vertical shifts of a function? 2. How does adding or subtracting a constant to a function affect its graph? 3. How can you determine the rule for a function given two tables of values? 4. What other transformations can be derived from table comparisons? 5. How can you reverse-engineer a function from its transformation? **Tip:** When finding transformations, always check each value systematically to see which transformation (like shifts or scaling) matches the new values.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Function transformations
Function composition

Formulas

-

Theorems

-

Suitable Grade Level

Grades 9-12

Related Recommendation

Analyzing Functions from Tables: g(x) and h(x) in terms of f(x)

Determine g(x) and h(x) in Terms of f(x) Using Function Tables

Determine the Function Transformation Relationship for h(x)

Find the relationship between h(x) and f(x)

Understanding Graph Transformations: Horizontal Reflections and Compressions