Answer with explanation:
There are two ways of solving this question
→Plot the graph of each of the function given,and check whether all the points that is, (-1,0), (1,-4), (2,-3), (4,5), (5,12), lie on which curve and then find appropriate curve which fits the data.
→Second method is, by substituting value of ordered pair in the given function, for which function all different x value is equal to different y value.
Function 1: [tex]f(x)= -x^2+2 x-3[/tex]
[tex]f(-1)= -(-1)^2+2\times(-1)-3\\\\= -1-2-3\\\\-6[/tex]
so, the point (-1,0) does not lie on the curve. We do not need to check further.So, the function [tex]f(x)= -x^2+2 x-3[/tex] will not pass through all the data points.This is not the appropriate function for the set of given data points.
Function 2: [tex]f(x)= x^2+2 x-3[/tex]
[tex]f(-1)= (-1)^2+2\times(-1)-3\\\\= 1-2-3\\\\-4[/tex]
so, the point (-1,0) does not lie on the curve. We do not need to check further.So, the function [tex]f(x)= x^2+2 x-3[/tex] will not pass through all the data points.This is not the appropriate function for the set of given data points.
Function 3: [tex]f(x)= -x^2-2 x-3[/tex]
[tex]f(-1)= (-1)^2-2\times(-1)-3\\\\= 1+2-3\\\\=0[/tex]
[tex]f(1)=-(1)^2-2(1)-3\\\\= -1-2-3\\\\=-6[/tex]
so, the point (1,-4) does not lie on the curve. We do not need to check further.So, the function [tex]f(x)= x^2+2 x-3[/tex] will not pass through all the data points.This is not the appropriate function for the set of given data points.
Function 4: [tex]f(x)= x^2-2 x-3[/tex]
[tex]f(-1)= (-1)^2-2\times(-1)-3\\\\= 1+2-3\\\\=3-3\\\\=0\\\\f(1)=(1)^2-2\times 1-3\\\\=1-2-3\\\\=-4\\\\f(2)=2^2-2\times 2-3\\\\=4-4-3\\\\=-3\\\\f(4)=4^2-2\times 4-3\\\\=16-8-3\\\\=5\\\\f(5)=5^2-5\times 2-3\\\\=25-10-3\\\\=12[/tex]
All the given set of points, (-1,0), (1,-4), (2,-3), (4,5), (5,12) lie on the curve [tex]f(x)= x^2-2 x-3[/tex].
Function 4 ,[tex]f(x)= x^2-2 x-3[/tex]. is appropriate model for the given data set of points.
Option D
