Answer:
<em>The Second Choice: g(x) = −2, x < −2</em>
<em>The Fourth Choice: g(x) = −2x + 6, x ≥ 1</em>
<em>The Fifth Choice: g(x) = x/2+ 1, –2 ≤ x < 1</em>
Step-by-step explanation:
<em>Important Note: you probably forgot to attach a graph of piece-wise function but after a little research I have found and </em><em>attached the graph</em><em> 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. </em>
<em>Solution:</em>
We have been given certain choices in the question and we have to select the correct choices based on <em>a graph of piece-wise function </em>as attached below.
<em>The first Choice: g(x) = −2x, −2 < x < 0</em>
<em>Answer is NO. </em>The reason is very simple. The function <em>g(x) = −2x </em>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.
<em>The Second Choice: g(x) = −2, x < −2</em>
<em>Answer is YES. </em>The reason is very simple. The function <em>g(x) = −2, x < −2 </em>indicates that it represents the horizontal line, being on the left side
of <em>x = -2 </em>and<em> </em>it is clearly shown the in given graph too.
<em>The Third Choice: </em>g(x) = x − 2, −2 < x < 1
<em>Answer is NO. </em>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.
<em>The Fourth Choice: g(x) = −2x + 6, x ≥ 1</em>
<em>Answer is YES. </em>Again, the reason is very simple. The function <em>g(x) = −2x + 6, x ≥ 1 clearly </em>indicates the downward graph. So, it is YES.
<em>The Fifth Choice: g(x) = x/2+ 1, –2 ≤ x < 1</em>
<em>Answer is YES. T</em>he reason is very simple. The function <em>g(x) = −2x + 6, x ≥ 1 clearly </em>indicates the downward graph. So, it is YES.
Keywords: function
, graph
<em>Learn more</em><em> about function graphs from brainly.com/question/11220142</em>
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