Question

1. kyle sketched the two graphs shown to the right. if the graph below the x - axis was his original function, f(x), which of the following would be the other function graphed, f(-x) or -f(x)? how do you know? 2. use the sketch of each given function to create the following transformations. label each line segment.

Explanation:

Step1: Recall transformation rules

The graph of $y = f(-x)$ is a reflection of $y = f(x)$ across the $y$-axis. The graph of $y=-f(x)$ is a reflection of $y = f(x)$ across the $x$-axis.

Step2: Analyze the given graphs

If the original function $f(x)$ is below the $x$-axis and the other function is above the $x$-axis in the corresponding $x -$ values, it is a reflection across the $x$-axis. So the other function is $-f(x)$.

Answer:

The other function is $-f(x)$ because it is a reflection of $f(x)$ across the $x$-axis.