Questions: Determine whether the following statement is true or false. Every graph represents a function. Choose the correct answer below. A. The statement is false because a graph that crosses the y-axis two times does not represent a function. B. The statement is true because every graph associates a unique y-value for each x-value. C. The statement is false because a graph that crosses the x-axis two times does not represent a function. D. The statement is true because every graph associates a unique x-value for each y-value.

Solution Steps

To determine whether the statement is true or false, we need to recall the definition of a function. A function is a relation where each input (x-value) is associated with exactly one output (y-value). Therefore, a graph represents a function if and only if no vertical line intersects the graph at more than one point. This is known as the vertical line test.

A function is defined as a relation where each input \( x \) is associated with exactly one output \( y \). This means that for any given \( x \)-value, there can only be one corresponding \( y \)-value.

To determine if a graph represents a function, we can use the vertical line test. If any vertical line intersects the graph at more than one point, then the graph does not represent a function. Specifically, if a graph crosses the \( y \)-axis two times, it fails this test.

• Option A states that the statement is false because a graph that crosses the \( y \)-axis two times does not represent a function. This is correct based on our understanding of functions.
• Option B incorrectly claims that every graph associates a unique \( y \)-value for each \( x \)-value, which is not true for all graphs.
• Option C incorrectly states that crossing the \( x \)-axis two times affects whether a graph is a function, which is irrelevant to the definition.
• Option D incorrectly claims that every graph associates a unique \( x \)-value for each \( y \)-value, which is also not true for all graphs.

Final Answer