Math Problem Statement

Evaluate and graph the linear function f(x) = -x - 8 using the provided table of values and graph points.

Solution

The problem involves evaluating and plotting the function f(x)=x8f(x) = -x - 8. A table of values is provided to calculate f(x)f(x) for specific xx-values, and the task is likely to graph these points on the coordinate plane provided.

Step-by-step Explanation:

1. Given Function:

f(x)=x8f(x) = -x - 8

2. Complete the Table:

For each value of xx, substitute it into the equation f(x)=x8f(x) = -x - 8:

  • For x=4x = -4: f(4)=(4)8=48=12f(-4) = -(-4) - 8 = 4 - 8 = -12
  • For x=8x = 8: f(8)=(8)8=88=20f(8) = -(8) - 8 = -8 - 8 = -20
  • For x=16x = 16: f(16)=(16)8=168=24f(16) = -(16) - 8 = -16 - 8 = -24

The table values are:

\hline x & f(x) \\ \hline -4 & -12 \\ 8 & -20 \\ 16 & -24 \\ \hline \end{array}$$ #### 3. **Plot Points on the Graph**: You should plot the points: - $$(-4, -12)$$ - $$(8, -20)$$ - $$(16, -24)$$ #### 4. **Draw the Line**: Since $$f(x) = -x - 8$$ is a linear function, the points will form a straight line when connected. Would you like help sketching the graph or further explanations? --- ### **Related Questions**: 1. How do you determine the slope and intercept of a linear function like $$f(x) = -x - 8$$? 2. What does the slope of $$-1$$ indicate about the graph's behavior? 3. How do you find additional points for $$f(x) = -x - 8$$? 4. Why is $$f(x) = -x - 8$$ considered a linear function? 5. How does the $$-8$$ in the equation affect the graph? --- ### **Tip**: For any linear function in the form $$y = mx + b$$, $$m$$ is the slope, and $$b$$ is the y-intercept.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Graphing
Slope-Intercept Form

Formulas

f(x) = mx + b
f(x) = -x - 8

Theorems

Slope-Intercept Form Theorem

Suitable Grade Level

Grades 8-10