Answer:
The correct option is 3.
Step-by-step explanation:
The parent function is
[tex]f(x)=|x|[/tex]
The horizontal stretch and compression is defined as
[tex]g(x)=|bx|[/tex]
If 0<b<1, then it is horizontal stretch and if b>1, then it is horizontal compression.
Graph 1 passing thought the point (1,-1).
[tex]-1=|b(1)|[/tex]
This statement is false for any value of b, because the value of modulus can not be negative.
Graph 2 passing thought the point (1,2).
[tex]2=|b(1)|[/tex]
[tex]2=b[/tex]
Since b>1, therefore this graph represent the horizontal compression.
Graph 3 passing thought the point (2,1).
[tex]1=|b(2)|[/tex]
[tex]\frac{1}{2}=b[/tex]
Since 0<b<1, therefore this graph represent the horizontal stretch.
Thus, the correct option is 3.
