To find the graph of \( f(-x) \) given that \( f(x) = x + 1 \), we substitute \(-x\) into the function:
\[ f(-x) = -x + 1 \]
This represents a linear function with a slope of \(-1\) and a y-intercept of \(1\). The original line, \(f(x) = x + 1\), has a positive slope and goes upwards from left to right. The graph of \(f(-x)\) will reflect this across the y-axis, resulting in a line that slopes downwards from left to right.
To select the correct graph from the options provided, look for a line that intersects the y-axis at \(1\) and slopes downwards:
- If option 1 depicts a line with a positive slope, it cannot be \(f(-x)\).
- If option 2 depicts a line with a positive slope, it cannot be \(f(-x)\).
- If option 3 has a y-intercept at \(1\) with a negative slope, that is a candidate for \(f(-x)\).
- If option 4 exhibits a positive slope, it cannot be \(f(-x)\).
Based on this analysis, if option 3 displays a line that goes through the point (0, 1) and slopes downward, this would be the correct representation of the graph of \( f(-x) \).
Therefore, the graph of \( f(-x) \) is option 3.