Q. 7 - Precalculus Enhanced with Graphing Utilities

Question

True or False: The graph of a function $y=f\left(x\right)$ always crosses the y-axis. 

Step-by-Step Solution

Answer

The statement is false.

Step 1. Definition

f is the symbol that we use to denote the function. It is symbolic of the equation (rule) that we use to get from an x in the domain to f(x) in the range.

Step 2. Final answer

If there exists a function that does not have a y-intercept then it will not crosses the y-axis.

Let the function is

$y=\frac{1}{x}$

The graph of this function never crosses the y-axis.

Therefore, the given statement "The graph of a function $y=f\left(x\right)$ always crosses the y-axis" is false.