You can try predicting the graph on some special points and will see it quickly the function which is plotted on the graph.
The rational function which is graphed below is given by
Option D: F(x)= 1/(x+2)(x-5)
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.
How to do analysis of the given graph to find the function it represents?
Since the graph is almost zero always except x = -2 and x = +5 ( since 5 lines are denoting 10,thus lines on x axis are made on two two intervals), thus the function must be such that as input increases, the output decreases quickly but stays above or below the x axis as per the interval.
The graph goes to +infinity or - infinity(depending on the sign of the function) as the input value x = -2 or + 5, this shows that there can be some value like (x + 2)(x- 5) in the denominator so that as x tends to -2 or +5, the denominator shrinks fast and therefore the function gets immensely big numbers.
I chose them since
[tex](x+2)(x-5)|_{x=-2} \: = (-2+2)(-2-5) = 0 \times -7 = 0\\\\(x+2)(x-5)|_{x=5} \: = (5+2)(5-5) = 7 \times 0 = 0[/tex]
As denominator goes to zero, the function will have big and big values.
We can see that when x < -2, the denominator [tex](x+2)(x-5)[/tex] is positive, and the function tends to upside, and when -2 < x < 5, the function is negative and when 5 < x, the function is positive again.
This shows that the function is having signs just like the denominator.
Thus, out of the options available, the fourth option seems so fit.
Thus,
The rational function which is graphed below is given by
Option D: F(x)= 1/(x+2)(x-5)
Learn more about functions and graphs here:
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