Answer:
- domain: -∞ < x < ∞
- range: -2 ≤ y < ∞
Explanation:
First of all, it is useful to understand what the graph is telling you. The curve tells you for input values between about -6.5 and -3.5, the output values are between -2 and about 7.5.
The arrow on the left end of the curve mean that as x goes more negative than -6.5, the y-value goes more positive than 7.5. The graph tends toward (-∞, ∞).
The arrow on the right end of the curve mean that as x goes more positive than -3.5, the y-value goes more positive than 7.5. The graph tends toward (∞, ∞).
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The question asks about the domain and range of the function.
The domain is the horizontal extent of the graph, a description of all possible input values for which the function is defined. Here, that is all possible values of x: the domain is -∞ < x < ∞.
The range is the vertical extent of the graph, a description of all possible output values from the function. Here, the function does not produce any outputs lower than -2, but it can give any value from -2 on upward: the range is -2 ≤ y < ∞.