Answer: Choice D)
The function has a range of all real numbers less than or equal to 2.
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Explanation:
Let's go through the answer choices to see which are true, and which are false.
- A) This is false because (0,-2) is a y intercept, and not an x intercept. A zero of a function is always an x intercept.
- B) This is false. The curve peaks at the vertex (2,2) showing we have a max point, and not a min point.
- C) This is false. A function can have at most one y intercept. If it had more than one y intercept, then it wouldn't be a function (since the input x = 0 leads to more than one output).
- D) This is true. The range is the set of possible y outputs. We see that y = 2 is the largest output, which occurs at the vertex. We can get anything smaller than this y value. Therefore, the range is the set of y values such that [tex]y \le 2[/tex]
