### All Precalculus Resources

## Example Questions

### Example Question #1 : Cartesian Coordinate System

The point is in which quadrant?

**Possible Answers:**

III

Lies on an axis

I

II

IV

**Correct answer:**

III

In order to determine in which quadrant the point lies, we must remember the order of the quadrants. The first quadrant is that where x and y are both positive, to the upper right of the origin. To move sequentially to the final quadrant, we go counterclockwise from the first quadrant, which means the second is where x is negative and y is positive, the third is where x and y are both negative, and the fourth is where x is positive and y is negative. We can see from our point (-3,-8) that x and y are both negative, which means the point lies in the third quadrant.

### Example Question #2 : Cartesian Coordinate System

and are located on the circle, with forming its diameter. What is the area of the circle.

**Possible Answers:**

**Correct answer:**

Use the distance formula to find the length of .

.

Since the length of is that of the diameter, the radius of the circle is .

Thus, the area of the circle is

.

### Example Question #3 : Cartesian Coordinate System

Which of the following coordinates does NOT fit on the graph of the corresponding function?

**Possible Answers:**

**Correct answer:**

When looking at the graph, it is clear that when , has a value less than . If we were to plug in the value of , our equation would come out as such:

Therefore, at , we get a , providing the coordinate .

### Example Question #4 : Cartesian Coordinate System

Which of the following coordinates does NOT correspond with the given function and graph?

**Possible Answers:**

**Correct answer:**

When looking at the graph, it is clear that when , has a value greater than . When we plug in both and values into the function, it is clear that these values do not work for the function:

### Example Question #5 : Cartesian Coordinate System

Which of the following coordinates does NOT correspond with the given function and graph?

**Possible Answers:**

**Correct answer:**

If we are to plug into our function, the values would not work and both sides of the equation would not be equal:

Therefore, we know that these coordinates do not lie on the graph of the function.

### Example Question #6 : Cartesian Coordinate System

Which of the following coordinates does NOT correspond with the given function and graph?

**Possible Answers:**

**Correct answer:**

If we were to plug in the coordinate into the function, we will find that it does not equate properly:

Since these values do not equate properly when plugged into the function, we now know that does not fit on the provided graph.

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