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Question

Part 1
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
negative 7
1
negative 3
2
1
3
5
4
9
Part 2
Plot each​ point, one at a time. Using the graphing​ tool, start by plotting ​(0,negative 7​).
.
.
.
Question content area right
Part 1
-10
-8
-6
-4
-2
2
4
6
8
10
-10
-8
-6
-4
-2
2
4
6
8
10
x
y

Answer 1

To approach this question, we will follow the provided instructions to plot each point from the data table and analyze the shape of the scatter plot to determine the best-fitting model (linear, exponential, logarithmic, or quadratic).

Here are the provided data points:

| x | y | |---|----------| | 0 | -7 | | 1 | -3 | | 2 | 1 | | 3 | 5 | | 4 | 9 |

Now, we will plot the points one by one.

1. Plot (0, -7)

   • This point is located where x = 0 (vertical), and y = -7 (horizontal).

2. Plot (1, -3)

   • Move right to x = 1, move up to y = -3.

3. Plot (2, 1)

   • Move right to x = 2, and then up to y = 1.

4. Plot (3, 5)

   • Move right to x = 3, and up to y = 5.

5. Plot (4, 9)

   • Move right to x = 4, and up to y = 9.

Once all these points are plotted on the graph, you will be able to observe their layout.

Analyzing the Scatter Plot:

1. Linear Function: If the points form a straight line.
2. Exponential Function: If the points curve upwards or downwards rapidly as x increases.
3. Logarithmic Function: If the points increase quickly initially and then level off.
4. Quadratic Function: If the points form a parabolic shape (opening upwards or downwards).

Analysis of Given Data:

Looking at the values of y as x increases:

• y starts at -7 when x is 0.
• As x increases, y increases from -7 to 9 in a fairly consistent manner.

Based on these changes (the difference in the y-values between each increment of x appears to increase):

• The relationship looks more like a quadratic or polynomial function rather than linear or exponential.

In summary, you'll likely find that the data is best modeled by a quadratic function. To confirm this, you could calculate the changes in y-values (first differences) and then the changes in those differences (second differences) to see if they are constant, which would indicate a quadratic relationship.

If you want to graph this and analyze the data visually, you should be able to determine the correct model more confidently based on the plotted points.