Question

Examine the graph. What is the domain and range of the function represented by the graph? Select two answers: one for the domain and one for the range.
domain: (−∞,∞)
range: [−9,∞)
domain: (−2,4)
range: (−∞,∞)
range: (−2,4)
domain: [−9,∞)

Answer 1

Answers:

domain: (−∞,∞)

range: [−9,∞)

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Explanation:

The graph extends forever to the left and right. This means any x value can be plugged into the function to get some y value output. The domain is the set of all real numbers in which we write (−∞,∞)  when using interval notation. This is the interval from negative infinity to positive infinity. We exclude both endpoints as we cannot reach infinity.

The smallest y value possible is y = -9 as shown by the vertex point (1, -9) being the lowest point on the parabola. The range is the set of y values such that $y \ge -9$ so we say [−9,∞) in interval notation. This is the interval from -9 to infinity. The square bracket says to include -9 as part of the interval.