Answer:
The graph of the function is given below.
We are given the function, [tex]f(x)=\frac{-x^2+4x+6}{x+4}[/tex]
We see that, when x= 0, the value of the function is,
[tex]f(0)=\frac{-0^2+40+6}{x+0}[/tex] i.e. [tex]f(0)=\frac{6}{4}=\frac{3}{2}[/tex].
So, the y-intercept is [tex](0,\frac{3}{2})[/tex].
Also, the zeroes of the function are given by,
[tex]f(x)=\frac{-x^2+4x+6}{x+4}=0[/tex]
i.e.[tex]-x^2+4x+6=0[/tex]
i.e. (x+1.162)(x-5.162)=0
i.e. x= -1.162 and x= 5.162
Thus, the x-intercept are (0,-1.162) and (0,5.162).
The graph of the function is given below.
