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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 ∞.

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