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Determine which statements about the graph are true. Select all that apply.

Determine which statements about the graph are true. Select all that apply.-example-1
User Baseem Najjar
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1 Answer

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A parabola has one maximum or minimum depending on the direction of its concavity. If the concavity is down, then it has a maximum and if it is up it has a minimum. Either way this minimum or maximum will be located on its vertex.

The vertex of this parabola is located at (3,4). So the parabola has a maximum of 4.

With this information we can classify the first two options as true.

The zeros of a function are the values for which the y-axis is equal to zero. The number of real zeros will be equal to the number of times the function will cross the x-axis. Since the function crosses the x-axis twice, then it has two real zeros. So the third option will be true.

The range of the function are the possible values of the function on the y-axis. We can notice that the function doesn't have any possible values above 4. The arrows on the lower side of the function represent that the function goes beyond what is displayed down. So its range will go from minus infinity to 4. Therefore, the fourth option will not be true.

The domain of the function are the possible values of the x-axis that can be used as an input for the function. Since the function goes beyond what is displayed on the graph until inifinity for both sides, then the domain of the function goes from minus infinity to infinity. Therefore the fith option will be true.

The function has two sections, the first one is increasing from minus infinity to 3 and the second one is decreasing from 3 to infinity. So the sixth option will not be true.

User Shudhansh Shekhar
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