### All GMAT Math Resources

## Example Questions

### Example Question #101 : Coordinate Geometry

What are the and intercepts of the function ?

**Possible Answers:**

y-intercept at

x-intercept at

y-intercept at

x-intercept at

y-intercept at

x-intercept at

None of the other answers

**Correct answer:**

None of the other answers

The correct answer is

y-intercept at

x-intercept at

To find the y-intercept, we plug in for and solve for

So we have . This is as simplified as we can get.

To find the x-intercept, we plug in for and solve for

So we have

(Exponentiate both sides)

( is 1, and cancel the and ln on the right side)

### Example Question #102 : Coordinate Geometry

Fill in the circle with a number so that the graph of the resulting equation has -intercept :

**Possible Answers:**

**Correct answer:**

Let be the number in the circle. The equation can be written as

Substitute 0 for and 5 for ; the equation becomes

### Example Question #111 : Coordinate Geometry

Fill in the circle with a number so that the graph of the resulting equation has -intercept :

**Possible Answers:**

The graph cannot have as its -intercept regardless of the value written in the circle.

**Correct answer:**

Let be the number in the circle. The equation can be written as

Substitute 0 for and 6 for ; the resulting equation is

24 is the correct choice.

### Example Question #112 : Coordinate Geometry

Fill in the circle with a number so that the graph of the resulting equation has -intercept :

**Possible Answers:**

The graph cannot have as its -intercept regardless of the value written in the circle.

**Correct answer:**

Let be the number in the circle. The equation can be written as

Substitute 0 for and for ; the resulting equation is

is the correct choice.

### Example Question #113 : Coordinate Geometry

Fill in the circle with a number so that the graph of the resulting equation has -intercept :

**Possible Answers:**

The graph cannot have as its -intercept regardless of the value written in the circle.

**Correct answer:**

The graph cannot have as its -intercept regardless of the value written in the circle.

Let be the number in the circle. The equation can be written as

Substitute 0 for ; the resulting equation is

The -intercept is regardless of what number is written in the circle.

### Example Question #114 : Coordinate Geometry

Fill in the circle with a number so that the graph of the resulting equation has -intercept :

**Possible Answers:**

**Correct answer:**

Let be the number in the circle. The equation can be written as

Substitute 7 for and 0 for ; the resulting equation is

35 is the correct choice.

### Example Question #115 : Coordinate Geometry

Fill in the circle so that the graph of the resulting equation has no -intercepts:

**Possible Answers:**

The graph will have at least one -intercept regardless of the value written in the circle.

**Correct answer:**

Let be the number in the circle. Then the equation can be rewritten as

Substitute 0 for and the equation becomes

Equivalently, we are seeking a value of for which this equation has no real solutions. This happens in a quadratic equation if and only if

Replacing with 4 and with 6, this becomes

Therefore, must be greater than . The only choice fitting this requirement is 4, so this is correct.

### Example Question #116 : Coordinate Geometry

Fill in the circle so that the graph of the resulting equation has exactly one -intercept:

**Possible Answers:**

None of the other choices is correct.

**Correct answer:**

None of the other choices is correct.

Let be the number in the circle. Then the equation can be rewritten as

Substitute 0 for and the equation becomes

Equivalently, we are seeking a value of for which this equation has exactly one solution. This happens in a quadratic equation if and only if

Replacing with 4 and with 8, this becomes

Therefore, either or .

Neither is a choice.

### Example Question #117 : Coordinate Geometry

Find the for the following equation:

**Possible Answers:**

**Correct answer:**

To find the , you must put the equation into slope intercept form:

where is the intercept.

Thus,

Therefore, your is

### Example Question #118 : Coordinate Geometry

Find where g(x) crosses the y-axis.

**Possible Answers:**

**Correct answer:**

Find where g(x) crosses the y-axis.

A function will cross the y-axis wherever x is equal to 0. This may be easier to see on a graph, but it can be thought of intuitively as well. If x is 0, then we are neither left nor right of the y-axis. This means we must be on the y-axis.

So, find g(0)

So our answer is 945.

Certified Tutor

Certified Tutor