Kim's flower was 2 inches high when she got it. It grew 0.75 inches per month until it was 12 months old. She keeps track of her flower's growth on a coordinate grid by graphing its height every two months and connecting the points to show the growth in between months.
Which statements are true? (Choose 3)
Responses
The function is increasing over time.
The function is discrete.
The function is Nonlinear.
The function is decreasing over time.
The function is Linear.
The functions is continuous.
1. The function is increasing over time.
2. The function is discrete.
3. The function is nonlinear.
The statements that are true are:
1) The function is increasing over time. This is because the flower's height is growing at a rate of 0.75 inches per month.
2) The function is discrete. The flower's height is recorded every two months, which means the data points are not continuous but rather spaced out.
3) The function is nonlinear. A linear function would have a constant rate of growth, but in this case, the height is increasing by 0.75 inches per month, indicating a changing rate of growth.
To determine which statements are true, let's analyze the given information.
First, we know that the flower's height grew by 0.75 inches per month. This indicates that the growth is constant and consistent.
Based on this, we can conclude:
1. The function is increasing over time: This statement is true because the flower's height is growing every month.
2. The function is discrete: This statement is false. A discrete function consists of individual points without any connected pattern. In this case, the growth of the flower is continuous as it increases by a fixed amount each month.
3. The function is nonlinear: This statement is false. A nonlinear function does not follow a straight line. In this case, the growth of the flower is linear because it increases by a fixed amount (0.75 inches) per month, forming a straight line on a graph.
4. The function is decreasing over time: This statement is false. The flower's height is explicitly stated to be growing, so it cannot be decreasing.
5. The function is linear: This statement is true. As mentioned earlier, the growth of the flower is consistent at a rate of 0.75 inches per month, following a straight line when plotted on a graph.
6. The function is continuous: This statement is true. The growth of the flower is uninterrupted and consistent, as it increases steadily every month without any gaps or breaks.
Therefore, the three true statements are:
- The function is increasing over time.
- The function is linear.
- The function is continuous.