Question

$f(x) = pm a |x - h| - k$ what does the \-\ in front of \a\ do to the graph?

1. shifts the graph down
2. reflects the graph across the x-axis
3. reflects the graph across the y-axis
4. shifts the graph left

Explanation:

For absolute value functions of the form $f(x) = a|x-h|+k$, a negative coefficient $-a$ flips the graph over the x-axis. This is because each y-value of the original function $f(x)=a|x-h|-k$ is multiplied by -1, reversing its sign relative to the x-axis. Reflecting over the y-axis would involve replacing $x$ with $-x$, which is not the case here. Vertical shifts are controlled by $k$, and horizontal shifts by $h$.

Answer:

reflects the graph across the x-axis