we are given
To find x-intercept means we have to find zeros
and for finding zeros , we will use quadratic formula
and we have it has two x-intercepts
so, it's discriminant must be greater than 0
so, we will find discriminant
now, we can compare with
and then we can find a , b and c
now, we can find D
It has two x-intercepts
so,
now, we can solve for m
............Answer
(1) Vertical asymptote:
(2) Domain:
(3) X intercept: and Y intercept :
(4) The function g(x) is shifted 4 units to the left and shifted 1 unit down.
Explanation:
The parent function is
The transformed function is
(1) Vertical asymptote:
The vertical asymptote of a function can be determined by equating
Thus,
The vertical asymptote is
(2) Domain:
The domain of a function is the set of all independent x-values.
Thus,
The domain of a function is
(3) X and Y intercepts:
To determine the x intercept, let us substitute y=0 in
Thus, the x intercept is
To determine the y intercept, let us substitute x=0 in
Thus, the y intercept is
(4) To determine the transformation:
The transformed function is shifted 4 units to the left and shifted 1 unit downwards.