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:

A function \( y = f(x) \) crosses the \( y \)-axis when \( x = 0 \). However, if \( 0 \) is not in the domain of the function \( f(x) \), then the graph of \( y = f(x) \) will not cross the \( y \)-axis. For example, consider the function \( y=\frac{1}{x} \). The domain of \( y = \frac{1}{x} \) is \( x
eq0 \). So, when \( x = 0 \), the function \( y=\frac{1}{x} \) is not defined. Thus, the graph of \( y=\frac{1}{x} \) does not cross the \( y \)-axis.

Answer:

False