Question

Find the domain and range and intercepts.g of x = 3 / x-4

Answer 1

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;

`\begin{gathered} y\text{ = }(3)/(x-4) \\ \end{gathered}`

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;

`\begin{gathered} y\text{ = }(3)/(0-4) \\ y\text{ = }(3)/(-4) \\ y\text{ = -0.75} \end{gathered}`