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Question

Which of the following will have their graph plotted in first and second quadrant only?
  1. |y|=f(|x|)
  2. y=f(|x|)
  3. |y|=f(x)
  4. y=|f(x)|


Solution

The correct option is D y=|f(x)|
In the first and second quadrant, y0
or y cannot be negative.
Let us take the equation
y=f((x|) means x can take any integer value and y will get values depending upon the function used. 
For example, if function is sine function. 
i.e., y=sin(|x|)
 y will get negative values also. Hence, its graph will lie in third and fourth quadrant also.

Similarly, in the graph of equation in option b and option c, the y can get negative values depending upon the function used.

In the option d, x can take any value, and f(x) also can be any real value. But y can be either zero or positive due to the modulus function.
Hence, the graph of y = |f(x)| will lie in first and second quadrant only.

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