Question

the entire graph of the function h is shown in the figure below. write the domain and range of h using interval notation. domain: range:

Explanation:

Step1: Determine the domain

The domain of a function is the set of all x - values for which the function is defined. Looking at the graph, the leftmost point has an open circle at \(x=-2\), so \(x > - 2\), and the rightmost point has an open circle at \(x = 4\), so \(x<4\). So the domain is the interval from \(-2\) (not including \(-2\)) to \(4\) (not including \(4\)). In interval notation, that is \((-2,4)\).

Step2: Determine the range

The range of a function is the set of all y - values that the function takes. Looking at the graph, the lowest y - value (from the left part) and the highest y - value (from the right part). The left part starts at an open circle with \(y=-3\) (so \(y > - 3\)) and the right part ends at an open circle with \(y = 4\) (so \(y<4\)). So the range is the interval from \(-3\) (not including \(-3\)) to \(4\) (not including \(4\)). In interval notation, that is \((-3,4)\).

Answer:

domain: \((-2, 4)\)
range: \((-3, 4)\)