Question

Write the following as inequalities Domain= Range=

Answer 1

Answer:

• domain: -∞ < x < ∞
• range: -2 ≤ y < ∞

Step-by-step 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 < ∞.