Question

A piecewise function g(x) is represented by the graph.

Answer 1

For different function different results are shown below.

What is Function?

A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B.

We have been given a graph of piecewise function. Using that we have to select the function from given choices which is represented by graph.

g(x) = −2x, −2 < x < 0

Answer:

NO. Because g(x) = −2x has negative slope so that means it goes downward also there is no y-intercept in g(x) = −2x but the only graph that has y-intercept in given graph goes upward so that can't be answer.

g(x) = −2, x < −2

Answer:

YES. Because g(x) = −2 is a horizontal line which is only on the left side of x=-2. Graph of this part is present in given graph. So yes it is answer.

g(x) = x − 2, −2 < x < 1

Answer:

NO. Because g(x) = x−2 has y-intercept at y=-2 and slope 1 so that means graph of g(x)= x-2 must be going upward and crossing at y=-2 but there is no such graph. Hence this can't be answer.

g(x) = −2x + 6, x ≥ 1

Answer:

YES. Because g(x) = −2x+6 satisfies the graph which is going downward.

g(x) = x/2+ 1, –2 ≤ x < 1

Answer:

YES. Because g(x) = x/2+ 1 satisfies the graph which is going downward.

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