Question

The graphs of two rational functions f and g are shown. Which function must be given by the expression of 10/x-3? Explain how you know.

Answer 1

Function is y = 10/x-3

-Find the domain of function:

we have that

`\begin{gathered} x-3\\e0 \\ x-3+3\\e0+3 \\ x\\e3 \end{gathered}`

Therefore

`x\in(-\infty,3)and(3,\infty)`

-Then find the range, this is

`y\in Real\text{ numbers}`

So, is the graph of the function f(x).

Answer. rational function f

Answer 2

A function that must be given by the expression of 10/x-3 is graph A because it has a vertical asymptote at x = 3.

In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).

By critically observing the rational function shown in the graph above, we can logically deduce that its vertical asymptotes can be determined by setting the denominator equal to zero and evaluating as follows;

x - 3 = 0

By adding 3 to both sides of the equation, we have the following;

x - 3 + 3 = 0 + 3

x = 3