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## Example Questions

### Example Question #1 : Dsq: Calculating X Or Y Intercept

What is the -intercept of a line with equation

1)

2)

**Possible Answers:**

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is not sufficient.

BOTH statements TOGETHER are NOT sufficient to answer the question.

EITHER Statement 1 or Statement 2 ALONE is sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient.

**Correct answer:**

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient.

The -intercept is the point at which . To find the -coordinate of the -intercept, just substitute 0 for :

Therefore, you need only know ; knowing is neither necessary nor helpful.

If you are given that since . the -intercept is easily determined to be .

The answer is that Statement 2 alone is sufficient, but not Statement 1 alone.

### Example Question #2 : Dsq: Calculating X Or Y Intercept

Give the -intercept of the graph of the equation .

Statement 1:

Statement 2:

**Possible Answers:**

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

**Correct answer:**

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

The -intercept of the graph of an equation is the point at which , so we evaluate :

The -intercept is simply the point , so knowing is necessary, and knowing is neither necessary nor helpful.

### Example Question #3 : Dsq: Calculating X Or Y Intercept

Find the -intercept and y-intercept of the following straight line.

1. The line has a slope of 0.6.

2. The line passes through point (10,2)

**Possible Answers:**

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

EACH statement ALONE is sufficient to answer the question asked.

**Correct answer:**

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

To find the - and y-intercepets, we need both statements of information.

Statement 1 is not enough information because we don't have a reference point for the slope. A slope by itself is not enough to define the line. There are an infinite amount of lines with a slope of 0.6.

Statement 2 is not enough information by itself since it only tells us about 1 point on the line. Again, there are an infinite number of lines that pass through the point (10,2).

Only by using both statements can we find the - and y-intercepts. Solving, we see the line is actually

### Example Question #4 : Dsq: Calculating X Or Y Intercept

Give the -intercept of the graph of the function

Statement 1:

Statement 2:

**Possible Answers:**

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

**Correct answer:**

To find the -intercept of , evaluate :

Knowing both and is necessary and sufficient.

### Example Question #5 : Dsq: Calculating X Or Y Intercept

Give the -intercept of the graph of the function

Statement 1:

Statement 2:

**Possible Answers:**

BOTH statements TOGETHER are insufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

**Correct answer:**

To find the -intercept of , evaluate :

Knowing is necessary and sufficient; the value of is irrelevant.

### Example Question #6 : Dsq: Calculating X Or Y Intercept

A line on the coordinate plane is neither horizontal nor vertical. Give its -intercept.

Statement 1: The line passes through .

Statement 2: The line passes through .

**Possible Answers:**

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

**Correct answer:**

Two points are necessary and sufficient to define a line. Therefore, neither statement alone is sufficient to determine the line, but both are sufficient. Once the line is defined, the -intercept - the point at which the line intersects the -axis - can be determined.

### Example Question #7 : Dsq: Calculating X Or Y Intercept

and are two distinct nonvertical lines on the coordinate plane.

True or false: and have the same -intercept.

Statement 1: and intersect at .

Statement 2: and are perpendicular.

**Possible Answers:**

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

**Correct answer:**

The question is equivalent to asking whether the lines intersect at a point on the -axis.

Assume Statement 1 alone. Since and are distinct lines, , their common -intercept, is their sole point of intersection. They cannot intersect at a second point, so they cannot have the same -intercept.

Assume Statement 2 alone. Perpendicular lines are lines that meet at right angles; the question of their point of intersection is not answered by this statement.

### Example Question #8 : Dsq: Calculating X Or Y Intercept

A function is graphed on the coordinate plane. Give the -intercept of the graph.

Statement 1:

Statement 2:

**Possible Answers:**

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

**Correct answer:**

The -intercept of the graph of is the point at which it intersects the -axis. Since this point has -coordinate 0, the -coordinate is . Statement 1 does not give us this value, but Statement 2 does.

### Example Question #9 : Dsq: Calculating X Or Y Intercept

and are two distinct nonvertical lines on the coordinate plane.

True or false: and have the same -intercept.

Statement 1: and have different -intercepts.

Statement 2: and both have slope .

**Possible Answers:**

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

**Correct answer:**

The question is equivalent to asking whether the lines intersect at a point on the -axis.

Statement 1 only establishes that the lines pass through different points on the -axis; no clues are given about any of their other points.

Statement 2 establishes that the lines have the same slope, and, subsequently, are parallel - that is, they do not intersect at all. Therefore, they cannot have the same -intercept.

### Example Question #10 : Dsq: Calculating X Or Y Intercept

Continuous function has the set of all real numbers as its domain.

How many -intercepts does the graph have?

Statement 1: If , then .

Statement 2: .

**Possible Answers:**

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

**Correct answer:**

BOTH statements TOGETHER are insufficient to answer the question.

The two statements together prvide insufficient information.

Assume both statements are true. By Statement 1, is a constantly increasing function, so it can intersect the -axis at most one time.

Now examine these two cases.

Case 1:

.

Also, if , then , so .

Since , the function has exactly one -intercept.

Case 2:

Also, if , then , so .

However, 2 raised to any power must be positive, so there is no value for which . The function has no -intercepts.

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