Video Transcript
The graph shows the function π of
π₯ equals π₯ squared minus two π₯ plus three. What is the solution set of π of
π₯ equals zero.
Given some graph of a function π¦
equals π of π₯, the solutions to the equation π of π₯ equals zero correspond to
the values of the π₯-intercepts if they exist. If there are no π₯-intercepts, it
follows that there are no solutions to the equation π of π₯ equals zero. Now in this case, weβve been given
the graph of the function π of π₯ equals π₯ squared minus two π₯ plus three and
asked to solve π of π₯ equals zero or, in other words, π₯ squared minus two π₯ plus
three equals zero.
But if we look carefully, we see
that there are no locations where the graph, which is the green plot here,
intersects the π₯-axis. And so, there are no real solutions
to the equation π of π₯ equals zero. In order to use set notation, we
need to find a way to show that there are no values inside the set. So we use the notation shown. Itβs the null set or empty set.
