Question

what is the domain of the function on the graph?

all real numbers
all real numbers greater than or equal to -2
all real numbers greater than or equal to -5
all real numbers greater than or equal to 0

Explanation:

Identify the function type and graph features

The graph shows a V-shaped curve, which represents an absolute value function of the form \(y = |x| - 2\). The vertex of this graph is located at \((0, -2)\). The graph extends infinitely to the left and to the right, as indicated by the arrows on both ends of the V-shape.

Define domain of a function

The domain of a function is the complete set of possible values of the independent variable, typically \(x\), for which the function is defined. On a coordinate plane, this corresponds to all the \(x\)-values covered by the graph from left to right.

Analyze the horizontal span of the graph

Looking at the graph, the left side of the V-shape has an arrow pointing upwards and to the left, meaning it continues infinitely in the negative \(x\)-direction (\(x \to -\infty\)). The right side of the V-shape has an arrow pointing upwards and to the right, meaning it continues infinitely in the positive \(x\)-direction (\(x \to \infty\)).

Determine the final domain

Since the graph covers every possible value along the horizontal \(x\)-axis without any breaks, holes, or vertical asymptotes, the domain of the function is all real numbers.

Answer:

• all real numbers (Correct answer)
• all real numbers greater than or equal to -2
• all real numbers greater than or equal to -5
• all real numbers greater than or equal to 0