Answer:
1. x=0
2. x>0
3. X-intercept: (0.5,0) Y-intercept: undefined
4. Compressed horizontally by a factor of 0.25 and shifted 1 unit down.
Step-by-step explanation:
1. The given parent function is
The transformed function is
The vertical asymptote is x=0.
We find this by equating the argument to zero. 4x=0----->x=0
2. The domain is all values of x that make the function defined.
The domain is
3. To find x-intercept we substitute g(x)=y=0 and solve for x.
x=0.5
The x-intercept is (0.5,0)
The y-intercept is undefined because we have to substitute x=0, which is not in the domain of g(x).
4. We can rewrite the transformed function in terms of f(x) as
This means there is a horizontal compression by and shift 1 unit down of the parent function.