Video Transcript
Determine the domain of the
function represented in the graph below.
We begin by recalling that the
domain of a function 𝑓 is the set of all 𝑥-values or inputs for which 𝑓 of 𝑥 is
defined. The solid dot at the far left of
our curve lies at the point with coordinates four, one. This means that when 𝑥 equals
four, 𝑦 is equal to one. And using function notation, 𝑓 of
four equals one.
The arrow at the other end of our
curve tells us that the function is defined for all real numbers to the right of
this point. And we can therefore conclude that
the function is defined for all values of 𝑥 greater than or equal to four. Had the dot at the point four, one
been hollow, then 𝑓 of 𝑥 would’ve been defined on the strict inequality 𝑥 is
greater than four. This inequality 𝑥 is greater than
or equal to four is the domain of the function. And we can also write this using
interval notation. The domain of the function
represented in the graph is the left-closed, right-open interval from four to ∞.
