GATE Mechanical 2018 Set 1 | GA | Question: 9

Question

Which of the following functions describe the graph shown in the below figure?

• A. $y=\mid \mid x \mid + 1 \mid -2$
• B. $y=\mid \mid x \mid - 1 \mid -1$
• C. $y=\mid \mid x \mid + 1 \mid -1$
• D. $y=\mid \mid x - 1 \mid -1\mid$

Answer 1

Take $x = 1$

$y_A = 0, y_B = -1, y_C =1, y_D =1$

Only $y_B$ is correct.

So, Option: B.

Comments

@Arjun sir

After getting $y_{b}=-1$ by putting $x=1$, how we are concluding that B is the option.

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@Kushagra गुप्ता

When we put $x = 1,$ then option $(B)$ given $ y = -1$

When we put $x = -1,$ then option $(B)$ given $ y = -1$

When we put $x = 0,$ then option $(B)$ given $ y = 0$

When we put $x = 2,$ then option $(B)$ given $ y = 0$

When we put $x = -2,$ then option $(B)$ given $ y = 0$

When we put $x = 3,$ then option $(B)$ given $ y = 1$

When we put $x = -3,$ then option $(B)$ given $ y = 1$

Only Option $(B)$ satisfies the given graph.

Answer 2

To solve this question we can use elimination method  

That is by substituting the values from the graph into the equations and check wheather they satisfy the equation or not

 

So 1st we can see that when x=0 then y=0 . So if we substitute x=0 in the equations then we should get y=0  

From this we can eliminate option-A because it is giving y=-1  

 

Next we can see that when x=-1 then y=-1. So if we substitue x=-1 then we can clearly see that only option-B gives y=-1  

so correct answer is option-B

Answer 3

solve by taking x=1 then y=-1

A: 0

B: -1

C:1

D: 1

So B is answer

Answer 4

 

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We can approach this question intuitively by observing the transformation of the graphs corresponding to each option.

• Options B and D are the only ones that produce a “W”-shaped graph.

• However, in Option D, the modulus is applied to the entire expression. This means the entire graph will stay above the X-axis.

• Option A does not have a y-intercept at 0 (it does not pass through the origin), so it can be eliminated.

• Option C simply represents ∣x∣, which does not match the required shape.

Given these observations, Option B is the only one that satisfies all the required conditions.

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