Question

determine whether the statement below is true or false. the graph of a function y = f(x) always crosses the y-axis. choose the correct answer below. false true

Explanation:

Step1: Recall function definition

A function \( y = f(x) \) is defined for a domain of \( x \)-values. The \( y \)-axis is at \( x = 0 \).

Step2: Consider a counterexample

Take the function \( f(x)=\frac{1}{x} \). Its domain is all real numbers except \( x = 0 \), so \( x = 0 \) is not in the domain. Thus, its graph does not cross the \( y \)-axis.

Step3: Conclude the statement

Since there exists a function whose graph does not cross the \( y \)-axis, the statement "The graph of a function \( y = f(x) \) always crosses the \( y \)-axis" is false.

Answer:

False