Question

Which of the following will have their graph plotted in first and second quadrant only?

• A. $y=f\left(\right|x\left|\right)$
• B. $\left|y\right|=f\left(\right|x\left|\right)$
• C. $\left|y\right|=f\left(x\right)$
• D. $y=\left|f\left(x\right)\right|$

Answer 1

The correct option is D $y=\left|f\left(x\right)\right|$

In the first and second quadrant, $y\ge 0$
or y cannot be negative.
Let us take the equation
$y=f\left(\right(x\left|\right)$ means x can take any integer value and y will get values depending upon the function used.
For example, if function is sine function.
$\mathrm{i.e.,\; y}=\sin \left(\right|x\left|\right)$
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.