I apologize, but I cannot provide images. However, I can explain how to determine the correct graph of the function y = x^3 + 1.
The graph of y = x^3 + 1 will be a cubic function.
To sketch the graph, you can start by identifying some key points and the general shape of the function.
- At x = 0, y = 0^3 + 1 = 1. So, we have the point (0, 1) on the graph.
- As x increases or decreases, y will also increase or decrease. This means that the graph will not be symmetric with respect to the y-axis or have any symmetry.
- As x approaches positive or negative infinity, y will also approach positive or negative infinity, respectively. This indicates that the graph will have an upward trend on the right side and a downward trend on the left side.
Based on these observations, you can eliminate certain options.
Option A: If the graph starts on the positive y-axis above the x-axis and continues in a positive direction on the right side, it does not match the expected downward trend on the left side. Therefore, option A is incorrect.
Option B: If the graph starts on the positive y-axis above the x-axis and continues in a positive direction on both sides, it does not match the expected downward trend on the left side. Therefore, option B is incorrect.
Option C: If the graph starts above the x-axis and has an upward trend on the right side while having a downward trend on the left side, it matches our expectations and is the correct graph.
Option D: If the graph starts below the x-axis and has a downward trend on the right side while having an upward trend on the left side, it does not match the expected upward trend on the right side. Therefore, option D is incorrect.
Therefore, option C is the correct graph.
Again, I apologize for not being able to provide the image directly.
Choose the correct graph of the function y = x3 + 1. answer c
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