The graph of the linear function f is shown, where \(\mathrm{y = f(x)}\). What is the x-intercept of the graph...

1. TRANSLATE the problem information

The question asks: "What is the x-intercept of the graph of f?"

• TRANSLATE this to mean: Find the point where the graph crosses the x-axis
• The x-intercept is always a point with coordinates \((x, 0)\) because \(y = 0\) on the x-axis
• We need to identify this crossing point from the graph

2. VISUALIZE the x-axis and locate the intersection point

• Look at the horizontal x-axis (the line where \(y = 0\))
• Trace the linear function from left to right
• The line starts in the lower left region and moves upward
• VISUALIZE where this line crosses the x-axis

3. Read the x-coordinate at the crossing point

• The line crosses the x-axis at \(x = -12\)
• At this point, \(y = 0\) (because it's on the x-axis)
• Therefore, the x-intercept is the point \((-12, 0)\)

Answer: A. \((-12, 0)\)

Why Students Usually Falter on This Problem

Most Common Error Path:

TRANSLATE error - Confusing x-intercept with y-intercept:

Students may misread "x-intercept" as "y-intercept" and instead look for where the graph crosses the y-axis (the vertical axis). Looking at the graph, the line appears to cross the y-axis at approximately \((0, 3)\). While this isn't one of the answer choices, this conceptual confusion causes students to become uncertain about what they're looking for.

This leads to confusion and guessing among the available choices.

Second Most Common Error:

VISUALIZE error - Misreading the grid scale or coordinates:

Students may correctly understand that they need the x-intercept but miscount the grid lines or misread the coordinate. For instance:

• They might identify the wrong grid line as -12
• They might confuse the intercept location with a nearby point on the line

This may lead them to select Choice D. \((12, 0)\) if they read the correct location but got the sign wrong (thinking positive 12 instead of negative 12).

The Bottom Line:

This problem tests whether students understand the definition of x-intercept and can accurately read coordinates from a graph. The key is knowing that "x-intercept" means where the graph crosses the x-axis (where \(y = 0\)), not the y-axis.