Question
The table shows points on the graph of an exponential function. Plot the points from the table on the graph.
x f(x)
-1 -8.667
0 -8
1 -6
2 0
3 18
x f(x)
-1 -8.667
0 -8
1 -6
2 0
3 18
Answers
GPT-4o mini
To plot the points from the table on a graph of an exponential function, you can follow these steps:
1. **Create a Coordinate System**:
- Draw a set of axes. The horizontal axis (x-axis) will represent the x-values and the vertical axis (y-axis) will represent the f(x) values.
2. **Label the Axes**:
- Mark the x-axis with a range that includes the values from the table (-1, 0, 1, 2, 3).
- Mark the y-axis with appropriate values to include the f(x) values from the table (-8.667, -8, -6, 0, 18).
3. **Plot the Points**:
- For each row in the table, plot the point (x, f(x)):
- For x = -1, f(x) = -8.667: Plot the point (-1, -8.667).
- For x = 0, f(x) = -8: Plot the point (0, -8).
- For x = 1, f(x) = -6: Plot the point (1, -6).
- For x = 2, f(x) = 0: Plot the point (2, 0).
- For x = 3, f(x) = 18: Plot the point (3, 18).
4. **Mark the Points**:
- Use dots or small circles to mark the locations of each point you plotted.
5. **Draw the Curve**:
- Since the function is exponential, connect the dots smoothly to reflect the continuous nature of the exponential function.
### Important Points to Note:
- Ensure that the scale of the axes is appropriate to accommodate all plotted points.
- Exponential functions typically exhibit a rapid increase or decrease, so you may notice this behavior between the points.
If you need to represent this graphically in software, you can use graphing tools like Desmos, GeoGebra, or even Excel to input the points and curve fitting features to create a better approximation of the function.
1. **Create a Coordinate System**:
- Draw a set of axes. The horizontal axis (x-axis) will represent the x-values and the vertical axis (y-axis) will represent the f(x) values.
2. **Label the Axes**:
- Mark the x-axis with a range that includes the values from the table (-1, 0, 1, 2, 3).
- Mark the y-axis with appropriate values to include the f(x) values from the table (-8.667, -8, -6, 0, 18).
3. **Plot the Points**:
- For each row in the table, plot the point (x, f(x)):
- For x = -1, f(x) = -8.667: Plot the point (-1, -8.667).
- For x = 0, f(x) = -8: Plot the point (0, -8).
- For x = 1, f(x) = -6: Plot the point (1, -6).
- For x = 2, f(x) = 0: Plot the point (2, 0).
- For x = 3, f(x) = 18: Plot the point (3, 18).
4. **Mark the Points**:
- Use dots or small circles to mark the locations of each point you plotted.
5. **Draw the Curve**:
- Since the function is exponential, connect the dots smoothly to reflect the continuous nature of the exponential function.
### Important Points to Note:
- Ensure that the scale of the axes is appropriate to accommodate all plotted points.
- Exponential functions typically exhibit a rapid increase or decrease, so you may notice this behavior between the points.
If you need to represent this graphically in software, you can use graphing tools like Desmos, GeoGebra, or even Excel to input the points and curve fitting features to create a better approximation of the function.