Respuesta :
a) Domain; all real numbers except 4
b) Range; all real numbers except y = 0
c) Y-intercept = -0.75
d) x-intercept does not exist
Here, we want to find the domain, range and intercepts
The domain refers to the possible x-values
From the question, the function will hold for all values of x, except x = 4, where we will have an undefined expression
Thus, the domain is all real numbers, except x= 4
For the range, we are referring to the possible y-values
From the given equation the possible y values are all real numbers except y = 0
To find the intercepts, let us write g(x) as y
The equation is thus;
[tex]\begin{gathered} y\text{ = }\frac{3}{x-4} \\ \end{gathered}[/tex]To get x-intercept, substitute y = 0
By doing this, we have no x-intercept
To get the y-intercept, we simply substitute x = 0
That means;
[tex]\begin{gathered} y\text{ = }\frac{3}{0-4} \\ y\text{ = }\frac{3}{-4} \\ y\text{ = -0.75} \end{gathered}[/tex]