Question

1. consider the graph.

which statement describes the graph correctly?

a the graph does not represent a function because for every input value, there is only one output value.

b the graph does not represent a function because for some input values, there is more than one output value.

c the graph represents a function because for every input value, there is only one output value.

d the graph represents a function because for some input values, there is more than one output value.

Explanation:

To determine if a graph represents a function, we use the vertical line test: a graph is a function if every vertical line intersects it at most once (i.e., each input \( x \)-value has exactly one output \( y \)-value).

• Option A: Claims the graph is not a function but gives a reason (one output per input) that defines a function. Eliminate A.
• Option B: Claims the graph is not a function, but the vertical line test (checking \( x \)-values) shows no \( x \) has multiple \( y \)-values. Eliminate B.
• Option C: States the graph is a function because each input has one output. This matches the vertical line test.
• Option D: Claims the graph is a function but gives a reason (multiple outputs for some inputs) that contradicts the definition of a function. Eliminate D.

Answer:

C. The graph represents a function because for every input value, there is only one output value.