Question

Matching

1.
y = -|2x|
2.
y = |-x|
3.
y = |-3x|

Answer 1

Do you want to match these to graphs? Here are concise descriptions you can use to match:

1) y = -|2x|
- Simplifies to y = -2|x|.
- Reflection across the x-axis and steeper than |x| (vertical stretch factor 2).
- Piecewise: y = 2x (x < 0), y = −2x (x ≥ 0).
- Vertex at (0,0); left branch slope 2, right branch slope −2.

2) y = |-x|
- |-x| = |x|, so this is just the standard absolute value.
- No reflection or stretch.
- Piecewise: y = −x (x < 0), y = x (x ≥ 0).
- Vertex at (0,0); left slope −1, right slope 1.

3) y = |-3x|
- |-3x| = 3|x|.
- Steeper than |x| (vertical stretch factor 3), no reflection.
- Piecewise: y = −3x (x < 0), y = 3x (x ≥ 0).
- Vertex at (0,0); left slope −3, right slope 3.

If you have three graphs to match, pick: the standard V for (2); the V reflected downward with slopes ±2 for (1); and the steepest upward V (slopes ±3) for (3). Send the graphs if you want me to match them explicitly.