Question: Question 9
Which expression reflects the graph of $f$ across the y-axis?
Option A
$-f(x)$
Option B
$f(x) - 1$
Option C
$f(-x)$
Option D
$f(x + 1)$
1. **State the problem:** We want to find which expression reflects the graph of $f$ across the y-axis.
2. **Recall the rule for reflection across the y-axis:** Reflecting a function $f(x)$ across the y-axis changes the input $x$ to $-x$. This means the reflected function is $f(-x)$.
3. **Analyze each option:**
- Option A: $-f(x)$ reflects the graph across the x-axis, not the y-axis.
- Option B: $f(x) - 1$ shifts the graph down by 1 unit.
- Option C: $f(-x)$ reflects the graph across the y-axis.
- Option D: $f(x + 1)$ shifts the graph left by 1 unit.
4. **Conclusion:** The correct expression for reflecting $f$ across the y-axis is $f(-x)$.
**Final answer:** Option C: $f(-x)$