GATE CE 2018 Set 1 — Question 8
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Engineering Mathematics → Calculus → Functions of Single Variable
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Question
Which of the following function(s) is an accurate description of the graph for the range(s) indicated?
(i) for
(ii) for
(iii) for
(iv) for
(ii) for
(iii) for
(iv) for
Correct answer
(B) (i), (ii) and (iv) only.
Solution
Let's evaluate each function against the provided graph:(i) For , the graph is a straight line passing through and .
Slope .
Equation: . This matches the graph. (Correct)(ii) For , .
At .
At .
At .
These points match the graph. (Correct)(iii) For , .
At .
However, the graph at shows . (Incorrect)(iv) For , the graph is a horizontal line at . This matches . (Correct)Functions (i), (ii), and (iv) are accurate descriptions. Thus, the correct option is (B).
Slope .
Equation: . This matches the graph. (Correct)(ii) For , .
At .
At .
At .
These points match the graph. (Correct)(iii) For , .
At .
However, the graph at shows . (Incorrect)(iv) For , the graph is a horizontal line at . This matches . (Correct)Functions (i), (ii), and (iv) are accurate descriptions. Thus, the correct option is (B).
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