Graph the function shown by the table. Tell whether the function is linear or nonlinear.
x|y
0|1
1|2
2|5
3|10
i'm sorry, i don't have the graph, but is their any way this could work without it? Please help. Thanks
No problem, I'm here to help! Based on the table, we can determine whether the function is linear or nonlinear without the need for a graph. In a linear function, the difference in y-values between any two points should be constant. Let's find out if that's the case.
The difference between the y-values for each pair of consecutive x-values is as follows:
1-0 = 1
2-1 = 1
5-2 = 3
10-5 = 5
Since the differences are not constant, we can conclude that the function is nonlinear.
Yes, it is possible to determine whether the function is linear or nonlinear without the graph.
To determine if a function is linear, we need to check if there is a constant rate of change between any two given points on the table.
Let's calculate the rate of change between consecutive points:
- From (0, 1) to (1, 2): (change in y) / (change in x) = (2 - 1) / (1 - 0) = 1 / 1 = 1
- From (1, 2) to (2, 5): (change in y) / (change in x) = (5 - 2) / (2 - 1) = 3 / 1 = 3
- From (2, 5) to (3, 10): (change in y) / (change in x) = (10 - 5) / (3 - 2) = 5 / 1 = 5
As we can see, the rate of change is not constant between the points: 1, 3, 5. Therefore, the function represented by the table is nonlinear.
y went up ONE from x = 0 to x = 1
BUT
y went up THREE from x = 1 to x = 2
therefore it is
NOT
linear, the slope changes
then it went up five from 2 to 3 just to make it painful.
You could do a parabola :)