Graphing Linear Function f(x) = -x

Math Problem Statement

Complete the table for the function f(x) = -x - 4 and graph the function.

To solve the given problem, we need to complete the table for the linear function $f(x) = -x - 4$ and plot the points on the graph.

Let's calculate $f(x)$ for each given $x$ value.

For $x = -2$ : $f(-2) = -(-2) - 4 = 2 - 4 = -2$ Ordered pair: $(-2, -2)$
For $x = -1$ : $f(-1) = -(-1) - 4 = 1 - 4 = -3$ Ordered pair: $(-1, -3)$
For $x = 0$ : $f(0) = -(0) - 4 = -4$ Ordered pair: $(0, -4)$
For $x = 1$ : $f(1) = -(1) - 4 = -1 - 4 = -5$ Ordered pair: $(1, -5)$
For $x = 2$ : $f(2) = -(2) - 4 = -2 - 4 = -6$ Ordered pair: $(2, -6)$

The completed table should look like this:

\hline x & f(x) & \text{Ordered Pair} \\ \hline -2 & -2 & (-2, -2) \\ -1 & -3 & (-1, -3) \\ 0 & -4 & (0, -4) \\ 1 & -5 & (1, -5) \\ 2 & -6 & (2, -6) \\ \hline \end{array}$$ Next, you can plot these points on the graph and draw a straight line through them to represent the linear function $$f(x) = -x - 4$$. Would you like further details on the graph or any questions about plotting? Here are 5 related questions to think about: 1. What is the slope of the function $$f(x) = -x - 4$$? 2. How does the graph of $$f(x) = -x - 4$$ compare to the graph of $$f(x) = x - 4$$? 3. What is the y-intercept of the function $$f(x) = -x - 4$$? 4. How does changing the value of $$-4$$ in the equation affect the graph? 5. What would the graph look like if the slope were positive instead of negative? **Tip:** The slope of a linear equation determines the steepness and direction (positive or negative) of the line.

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