Question

y=|-x|

Answer 1

The equation \( y = |-x| \) describes a V-shaped graph. To analyze it, we can break down the absolute value expression:

1. **Understanding the absolute value**: The absolute value \( |-x| \) is always non-negative and can be evaluated as follows:
- If \( x \geq 0 \), then \( |-x| = -x \) (since \(-x\) would be non-positive).
- If \( x < 0 \), then \( |-x| = x \) (because \(-x\) would be positive).

2. **Rewriting the function**:
- For \( x \geq 0 \):
\[
y = |-x| = -x
\]
- For \( x < 0 \):
\[
y = |-x| = x
\]

3. **Function Representation**:
Thus, we can write the function in piecewise form:
\[
y = \begin{cases}
-x & \text{if } x \geq 0 \\
x & \text{if } x < 0
\end{cases}
\]

4. **Graphing the function**:
- When \( x = 0 \), \( y = 0 \).
- As \( x \) increases, \( y \) decreases linearly with a slope of -1.
- As \( x \) decreases (moves left of the origin), \( y \) increases linearly with a slope of 1.

5. **Graph**:
The graph is symmetric about the y-axis, and it forms a "V" shape that opens upwards. The vertex of the "V" is at the origin (0,0).

In summary, the graph of \( y = |-x| \) is a V-shaped graph centered at the origin with the slopes of the lines being 1 and -1 on either side of the y-axis.