Identify the X-Value at the X-Axis Intersection on This Linear Graph

Let's proceed to identify the correct function corresponding to the graph:

The graph displays a "V" shape, which is a strong indicator of an absolute value function. To identify it, we must find its vertex.

Given the transformation properties of absolute values, the graph equation is of the general form $y = \lvert x - h \rvert + k$, where $(h, k)$ is the vertex.

• The vertex for the graph is found at $(1, 0)$.
• This means the function template follows $y = \lvert x - 1 \rvert$. This aligns with an $x$ translation of 1 to the right.

Checking the answer choices given:

• Choice (1): $y = x - 1$ - This represents a straight line, not an absolute value function.
• Choice (2): $y = x + 1$ - Incorrect due to the vertex position.
• Choice (3): $y = |1x|$ - Incorrect due to no translation present: the vertex is unaffected by modifying the coefficient of $x$.
• Choice (4): $y = \lvert x - 1 \rvert$ - Matches the $(1, 0)$ vertex position and absolute value function type.

Thus, the correct answer is $y = \lvert x - 1 \rvert$.