Question

Suppose $f$ is the collection of all ordered pairs of real numbers and $4x=6$ is the first element of some ordered pair in $f$. Suppose the vertical line through $x=6$ intersects the graph of $f$ twice. Is $f$ a function ? Why or why not If f is a function, enter 1 or else enter 0

Answer 1

First observe that the graph of the function $f$ consists of points represented by the ordered pairs of the form $(x,f(x\left)\right)$.If the vertical line through $x=6$ is cut by the graph of $f$ twice, then it means that the element 6 of the domain of $f$ has two images. Hence $f$ is not a function as for $f$ to be a function each element of the domain must have unique image.
Ans: 0