match the correct description to the graph

Question

x y
0 1
1 3
2 9
3 27
4 81

responses
nonlinear; not a function
nonlinear; function
linear; function
linear; not a function

Answer 1

To determine the correct description of the graph based on the given (x, y) values, let's analyze the data:

x    y
0    1
1    3
2    9
3    27
4    81

1. Check if it is a function: A relation is a function if each input (x value) pairs with exactly one output (y value). Each x value here corresponds to exactly one y value, so it is a function.

2. Check if it is linear or nonlinear: A linear relationship would show a constant rate of change. To see if this is linear, we can look for a constant difference between consecutive y values.

Let's look at the differences between the y values:

• Between x = 0 and x = 1: 3 - 1 = 2
• Between x = 1 and x = 2: 9 - 3 = 6
• Between x = 2 and x = 3: 27 - 9 = 18
• Between x = 3 and x = 4: 81 - 27 = 54

The differences are not constant; they are increasing. Therefore, the relationship is nonlinear.

Based on the analysis:

• The relationship is nonlinear.
• It is a function.

Thus, the correct description for the graph is "nonlinear; function."