Question

Match the following functions and their graph

Function	Graph
1) y = |sinx|	A)
2) y = sin |x|	B)
3) |y| = sinx	C)

• A. 1 - A, 2 - B, 3 - C
• B. 1 - C, 2 - B, 3 - A
• C. 1 - B, 2 - C, 3 - A
• D. 1 - C, 2 - A, 3 - B

Answer 1

The correct option is B 1 - C, 2 - B, 3 - A

We know the graph of y = sin(x). Given functions are obtained by applying modulus function on either x or y or on the sine function.
Hence, the graph of new function will be obtained by some transformations of y = sin(x) graph only.

Let us take y = | sin x |
It implies that the value of y can never be negative. Hence, the graph is obtained by inverting the negative part of y = sin (x) graph in the upward direction. It is shown in graph C.

Now, consider y = sin|x|,
|x| is always non-negative.
positive x and negative value of x will give same output.
So, to plot y = sin|x|, we will ignore the graph of y = sinx along negative x-direction and take the reflection of the graph which is along positive x-axis.
This implies that the graph will be symmetric about y-axis. Its graph is shown in figure B.

Similarly, consider |y| = sinx.
Here, $\mathrm{LHS}\ge 0$
So, we will ignore the graph where sinx is negative.
For the graph where sinx is non-negative, we have
$\left(y\right|=\mathrm{sinx}\Rightarrow y=\pm \mathrm{sinx}$
$y=-\mathrm{sinx},\mathrm{sinx}\ge 0$ can be plotted by taking reflection along x-axis. This implies that graph will be symmetric about x-axis.
So, the correct graph is figure A.