# GMAT Math : Calculating x or y intercept

## Example Questions

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### Example Question #701 : Geometry

What are the  and  intercepts of the function  ?

y-intercept at

x-intercept at

y-intercept at

x-intercept at

y-intercept at

x-intercept at

Explanation:

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 #11 : Calculating X Or Y Intercept

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

Explanation:

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 :

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

Explanation:

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 :

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

Explanation:

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 :

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

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

Explanation:

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 :

Explanation:

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:

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

Explanation:

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:

None of the other choices is correct.

None of the other choices is correct.

Explanation:

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:

Explanation:

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

where is the intercept.

Thus,

### Example Question #118 : Coordinate Geometry

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

Explanation:

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)