Math Problem Statement

Complete the function table for the function g(x) = x + 2.

Solution

The function g(x)=x+2g(x) = x + 2 is given, and we need to complete the function table by calculating g(x)g(x) for each value of xx.

Let's compute g(x)g(x) for each value:

  • For x=−5x = -5, g(−5)=−5+2=−3g(-5) = -5 + 2 = -3
  • For x=−1x = -1, g(−1)=−1+2=1g(-1) = -1 + 2 = 1
  • For x=0x = 0, g(0)=0+2=2g(0) = 0 + 2 = 2
  • For x=1x = 1, g(1)=1+2=3g(1) = 1 + 2 = 3
  • For x=2x = 2, g(2)=2+2=4g(2) = 2 + 2 = 4

Thus, the completed table is:

\hline x & g(x) \\ \hline -5 & -3 \\ -1 & 1 \\ 0 & 2 \\ 1 & 3 \\ 2 & 4 \\ \hline \end{array}$$ Would you like more details or have any questions? Here are five related questions to expand this topic: 1. What happens to $$g(x)$$ when $$x$$ increases by 1? 2. How would the function table look if the function was $$g(x) = x - 3$$? 3. How would the graph of $$g(x) = x + 2$$ look like? 4. What is the domain and range of this linear function? 5. How does the slope of $$g(x) = x + 2$$ influence its growth? **Tip**: When working with linear functions, the constant term shifts the graph vertically, while the coefficient of $$x$$ determines the slope or steepness.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions

Formulas

g(x) = x + 2

Theorems

Linear function properties

Suitable Grade Level

Grades 6-8

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