Answer :
When we talk about transforming points on a function's graph, each type of transformation affects the coordinates in specific ways. Let's examine each option to identify the correct transformation type:
A. Compressions:
- Compressions involve scaling the graph of a function towards the x-axis or y-axis by multiplying the coordinates by a factor between 0 and 1. This does not involve multiplying coordinates by -1.
B. Reflections:
- Reflections are transformations that flip the graph over a specific axis.
- Multiplying the [tex]\(x\)[/tex]-coordinate by [tex]\(-1\)[/tex] reflects the graph over the [tex]\(y\)[/tex]-axis.
- Multiplying the [tex]\(y\)[/tex]-coordinate by [tex]\(-1\)[/tex] reflects the graph over the [tex]\(x\)[/tex]-axis.
- Multiplying both coordinates by [tex]\(-1\)[/tex] reflects the graph over both axes, equivalent to a 180-degree rotation about the origin.
C. Stretches:
- Stretches involve scaling the graph away from the x-axis or y-axis by multiplying the coordinates by a factor greater than 1. This, like compressions, does not involve multiplying coordinates by -1.
D. Translations:
- Translations involve shifting the entire graph horizontally, vertically, or both without altering the shape or orientation of the graph. This type of transformation involves adding or subtracting constants from the coordinates but not multiplying them by -1.
Given these descriptions, we can see that Reflections (Option B) specifically involve multiplying one or both of the coordinates by [tex]\(-1\)[/tex], which flips the graph over the appropriate axis.
Thus, the correct answer is:
[tex]\[ \boxed{\text{B}} \][/tex]
A. Compressions:
- Compressions involve scaling the graph of a function towards the x-axis or y-axis by multiplying the coordinates by a factor between 0 and 1. This does not involve multiplying coordinates by -1.
B. Reflections:
- Reflections are transformations that flip the graph over a specific axis.
- Multiplying the [tex]\(x\)[/tex]-coordinate by [tex]\(-1\)[/tex] reflects the graph over the [tex]\(y\)[/tex]-axis.
- Multiplying the [tex]\(y\)[/tex]-coordinate by [tex]\(-1\)[/tex] reflects the graph over the [tex]\(x\)[/tex]-axis.
- Multiplying both coordinates by [tex]\(-1\)[/tex] reflects the graph over both axes, equivalent to a 180-degree rotation about the origin.
C. Stretches:
- Stretches involve scaling the graph away from the x-axis or y-axis by multiplying the coordinates by a factor greater than 1. This, like compressions, does not involve multiplying coordinates by -1.
D. Translations:
- Translations involve shifting the entire graph horizontally, vertically, or both without altering the shape or orientation of the graph. This type of transformation involves adding or subtracting constants from the coordinates but not multiplying them by -1.
Given these descriptions, we can see that Reflections (Option B) specifically involve multiplying one or both of the coordinates by [tex]\(-1\)[/tex], which flips the graph over the appropriate axis.
Thus, the correct answer is:
[tex]\[ \boxed{\text{B}} \][/tex]
