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. a. -f(x) b. f(-x)

Explanation:

Step1: Recall transformation rules

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

Step2: Analyze the given graphs

If the original function $f(x)$ is below the $x -$axis and the other graph is above the $x -$axis in a mirror - like way with respect to the $x -$axis, then the other function is $-f(x)$.

Step3: For part 2a

To graph $-f(x)$ for a given function $f(x)$, take each point $(x,y)$ on $f(x)$ and change it to the point $(x, - y)$. That is, reflect each point of $f(x)$ across the $x -$axis.

Step4: For part 2b

To graph $f(-x)$ for a given function $f(x)$, take each point $(x,y)$ on $f(x)$ and change it to the point $(-x,y)$. That is, reflect each point of $f(x)$ across the $y -$axis.

Answer:

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

2.
a. To graph $-f(x)$, reflect the given function across the $x -$axis.
b. To graph $f(-x)$, reflect the given function across the $y -$axis.