Question

Use the graphing tool at the right to create a scatter plot for the data in the table. Use the shape of the scatter plot to determine if the data are best modeled by a linear​ function, an exponential​ function, a logarithmic​ function, or a quadratic function.
x
y
0
0
4
0.6
9
1.0
17
1.2
23
1.4
Part 2
Plot each​ point, one at a time. Using the graphing​ tool, start by plotting ​(0,0).
.
.
.
Question content area right
Part 1
-6
-3
3
6
9
12
15
18
21
24
27
-0.6
-0.3
0.3
0.6
0.9
1.2
1.5
1.8
x
y

Answer 1

To create a scatter plot for the provided data set, we'll start by plotting each point one at a time, as you instructed. Here’s the data again for reference:

| x | y |
|----|-----|
| 0 | 0 |
| 4 | 0.6 |
| 9 | 1.0 |
| 17 | 1.2 |
| 23 | 1.4 |

Now let's plot the points step-by-step:

1. **Plot (0, 0)**: This is the origin of the plot, where both x and y values are 0.
2. **Plot (4, 0.6)**: This point is to the right of (0, 0) along the x-axis and slightly above it.
3. **Plot (9, 1.0)**: This point is further to the right on the x-axis and at 1.0 on the y-axis.
4. **Plot (17, 1.2)**: This point continues right on the x-axis and remains slightly above 1.0 on the y-axis.
5. **Plot (23, 1.4)**: This point is also further to the right and continues the upward trend, reaching 1.4 on the y-axis.

### Shape of the Scatter Plot:
Once you plot all these points, you can look at their overall arrangement to identify the trend.

From the values:
- As \( x \) increases, \( y \) increases, but the rate of increase appears to be slowing down (i.e., the increase in \( y \) is less than proportional to the increase in \( x \)).

### Analysis:
- **Linear Function**: Displays a constant rate of increase, which doesn't match our data.
- **Exponential Function**: Shows rapid growth, which also does not match the data.
- **Logarithmic Function**: Could be a candidate if the data level off significantly.
- **Quadratic Function**: Might fit if there is a parabolic trend, which does not appear evident here.

### Conclusion:
Based on the provided data points, the relationship seems to have a gradual increase that suggests a logarithmic or possibly quadratic function, but it is weaker than either. Notably, if we assume the data continues to form a clear increasing trend that slows down, a **logarithmic function** could be the best fit; however, further analysis with more data points or regression analysis would solidify the conclusion.

To visualize this accurately, you could utilize graphing software, a calculator, or tools like Desmos or GeoGebra to confirm the best fit for the line through regression analysis.