For questions 3–4, which kind of function best models the data in the table? Use differences or ratios.
x
y
0
–1
1
–0.5
2
0
3
0.5
4
1
(1 point)
A) linear
B)quadratic
C) exponential
D) none of these
To determine the type of function that best models the data in the table, we can examine the differences or ratios between consecutive y-values.
For differences:
The differences between the consecutive y-values are as follows:
-1 - (-1) = 0
-0.5 - (-1) = 0.5
0 - (-0.5) = 0.5
0.5 - 0 = 0.5
1 - 0.5 = 0.5
The differences between consecutive y-values are constant, which suggests a linear relationship.
For ratios:
The ratios between the consecutive y-values are as follows:
-1 / -1 = 1
-0.5 / -1 = 0.5
0 / -0.5 = 0
0.5 / 0 = undefined
1 / 0.5 = 2
The ratios between consecutive y-values are not constant, indicating that it is not an exponential relationship.
Based on the analysis of both the differences and ratios, we can conclude that a linear function best models the data in the table.
Therefore, the answer is A) linear.
(x , y ) points are (0 -1) (1 -.5) (2 , 0) (3, .5) (4,1)
slope of each other point from (0 ,-1) = (change in y / change in x)
m1 = (-.5 +1) / (1 - 0) = .5/1 = 1/2
m2 = (0 + 1) / (2 -0) = 1/2
....
m 5 = (1 + 1) / (4 - 0) = 1/2
remarkable, slope is 1/2 from the first point no matter where you look.
I think it might be a straight line.