To find the places where the graph of the function $y = 3 - x$ crosses the X-axis within the range $[0, 4]$ in steps of 0.2, we can follow these steps:

1. Understand the problem:

The graph of a function crosses the X-axis where $y = 0$. Thus, we need to find the value(s) of $x$ for which $y = 3 - x = 0$.

2. Solve for $x$ where $y = 0$:

$3 - x = 0$ $x = 3$ The graph crosses the X-axis at $x = 3$.

3. Evaluate the function in the given range:

We evaluate $y = 3 - x$ for $x$ in the range $[0, 4]$ in steps of 0.2:

\hline x & y = 3 - x \\ \hline 0 & 3 \\ 0.2 & 2.8 \\ 0.4 & 2.6 \\ 0.6 & 2.4 \\ 0.8 & 2.2 \\ 1 & 2 \\ 1.2 & 1.8 \\ 1.4 & 1.6 \\ 1.6 & 1.4 \\ 1.8 & 1.2 \\ 2 & 1 \\ 2.2 & 0.8 \\ 2.4 & 0.6 \\ 2.6 & 0.4 \\ 2.8 & 0.2 \\ 3 & 0 \\ 3.2 & -0.2 \\ 3.4 & -0.4 \\ 3.6 & -0.6 \\ 3.8 & -0.8 \\ 4 & -1 \\ \hline \end{array}$$ ### 4. **Determine where the graph crosses the X-axis:** The graph crosses the X-axis at $$x = 3$$, where $$y = 0$$. ### Conclusion: The graph of the function $$y = 3 - x$$ crosses the X-axis at $$x = 3$$. --- Would you like a more detailed explanation or do you have any questions? Here are some related questions for further exploration: 1. What is the slope of the line $$y = 3 - x$$? 2. How would the graph change if the function were $$y = 3 - 2x$$? 3. How can we find the intersection of the graph $$y = 3 - x$$ with another line, say $$y = x - 1$$? 4. What is the significance of the y-intercept in this function? 5. How does the function $$y = 3 - x$$ compare with the function $$y = x - 3$$? **Tip:** When finding where a graph crosses the X-axis, look for the point where the function equals zero.