Solution:
1. The given function is
f(x) = 2 x
it is equation of line passing through origin having slope 2 and the line passes through first and third quadrant.
Domain= All Real numbers, Range = All Real Numbers
2. Now , when x is replaced by (-12 x), we get
f(-12 x)= 2 × (-12 x)
Let f(-12 x)= f(z)= -24 x
it is equation of line passing through origin having slope -24 and the line passes through second and fourth quadrant.
Domain= All Real numbers, Range = All Real Numbers
Relation between the two function i.e between 1 and 2 is
→Slope of line 2 = Slope of line 1 × (-12)
→ The function 2 i.e f(z)= -24 x shifts in left Direction.
The function 1 is dilated by factor of (-12) to get function 2.