You can use the graph given to form the equation and using the fact that as the denominator goes towards zero, the fraction outputs immensely big magnitude numbers(tending to arbitrarily large numbers)
The equation for the given graph can be:
[tex]f(x) = \dfrac{1}{(x-1)} - 2[/tex]
How to find the function which was used to make graph?
There are many tools we can use to find the information of the relation which was used to form the graph.
A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.
If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.
Using the graph to form the equation
Since the graph goes to negative infinity as it comes from left side of 1 towards 1, and goes to positive infinity as it comes from the right side of 1, thus, there might be x-1 in denominator which takes the magnitude to infinite and sign to + if x > 1 and to - if x < 1
Now since the graph intersects the y axis at y = -3, thus, we need the function to be such that putting x = 0 in the function outputs -3 as value of the function.
Thus,
[tex]f(0) = -3[/tex]
Since putting 0 in [tex]\dfrac{1}{(x-1)}[/tex] gives -1 as answer, we have to subtract 2 more.
Thus, we have:
[tex]f(x) = \dfrac{1}{x-1} - 2[/tex]
Checking it, as the graph intersects the x axis at 1.5, putting f(x) = 0 should give us x = 1.5,
[tex]f(x) = \dfrac{1}{x-1} - 2\\\\0 = \dfrac{1}{x-1} - 2\\\\2(x-1) = 1\\\\x = 1 + \dfrac{1}{2} = 1.5[/tex]
It is correct.
Thus,
The equation for the given graph can be:
[tex]f(x) = \dfrac{1}{(x-1)} - 2[/tex]
Its graph is attached below.
Learn more about graphing functions here:
https://brainly.com/question/17056821
