Answer:
The Second Choice: g(x) = −2, x < −2
The Fourth Choice: g(x) = −2x + 6, x ≥ 1
The Fifth Choice: g(x) = x/2+ 1, –2 ≤ x < 1
Step-by-step explanation:
Important Note: you probably forgot to attach a graph of piece-wise function but after a little research I have found and attached the graph you probably had to attach. So, I am answering your question based on the reference of this graph I attached. Hopefully, it would help you clearing the concept.
Solution:
We have been given certain choices in the question and we have to select the correct choices based on a graph of piece-wise function as attached below.
The first Choice: g(x) = −2x, −2 < x < 0
Answer is NO. The reason is very simple. The function g(x) = −2x indicates that the graph must be downward as it carries negative slope, and having no y-intercept. But, if we check the attached graph it is clear that there is only graph having y-intercept goes upward. Hence, it can't be the answer.
The Second Choice: g(x) = −2, x < −2
Answer is YES. The reason is very simple. The function g(x) = −2, x < −2 indicates that it represents the horizontal line, being on the left side
of x = -2 and it is clearly shown the in given graph too.
The Third Choice: g(x) = x − 2, −2 < x < 1
Answer is NO. The reason is very simple. The function g(x) = x − 2, −2 < x < 1 indicates that it has the slope 1 and having y-intercept at y = -2. It means its graph should be upward and must have to cross the line at y = -2. But, the attached graph figure shows it does not have any such representation.
The Fourth Choice: g(x) = −2x + 6, x ≥ 1
Answer is YES. Again, the reason is very simple. The function g(x) = −2x + 6, x ≥ 1 clearly indicates the downward graph. So, it is YES.
The Fifth Choice: g(x) = x/2+ 1, –2 ≤ x < 1
Answer is YES. The reason is very simple. The function g(x) = −2x + 6, x ≥ 1 clearly indicates the downward graph. So, it is YES.
Keywords: function
, graph
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