### All Advanced Geometry Resources

## Example Questions

### Example Question #48 : Coordinate Geometry

Give the -coordinate of the -intercept of the graph of the function

**Possible Answers:**

**Correct answer:**

The -intercept of the graph of is the point at which it intersects the -axis. Its -coordinate is 0; its -coordinate is , which can be found by substituting 0 for in the definition:

### Example Question #49 : Coordinate Geometry

Give the -coordinate of the -intercept of the graph of the function .

**Possible Answers:**

The graph of has no -intercept.

**Correct answer:**

The -intercept of the graph of is the point at which it intersects the -axis. Its -coordinate is 0; its -coordinate is , which can be found by substituting 0 for in the definition:

,

the correct choice.

### Example Question #50 : Coordinate Geometry

Give the -coordinate of the -intercept of the graph of the function .

**Possible Answers:**

The graph of has no -intercept.

**Correct answer:**

The graph of has no -intercept.

The -intercept(s) of the graph of are the point(s) at which it intersects the -axis. The -coordinate of each is 0,; their -coordinate(s) are those value(s) of for which , so set up, and solve for , the equation:

Subtract 7 from both sides:

Divide both sides by 2:

The next step would normally be to take the natural logarithm of both sides in order to eliminate the exponent. However, the negative number does not have a natural logarithm. Therefore, this equation has no solution, and the graph of has no -intercept.

### Example Question #51 : Coordinate Geometry

Give the -coordinate of the -intercept of the graph of the function

**Possible Answers:**

**Correct answer:**

The -intercept(s) of the graph of are the point(s) at which it intersects the -axis. The -coordinate of each is 0,; their -coordinate(s) are those value(s) of for which , so set up, and solve for , the equation:

Add 8 to both sides:

Divide both sides by 2:

Take the common logarithm of both sides to eliminate the base:

### Example Question #52 : Coordinate Geometry

Give the domain of the function .

**Possible Answers:**

The set of all real numbers

**Correct answer:**

The set of all real numbers

Let . This function is defined for any real number , so the domain of is the set of all real numbers. In terms of ,

Since is defined for all real , so is ; it follows that is as well. The correct domain is the set of all real numbers.

### Example Question #53 : Coordinate Geometry

Give the range of the function .

**Possible Answers:**

The set of all real numbers

**Correct answer:**

Since a positive number raised to any power is equal to a positive number,

Applying the properties of inequality, we see that

,

and the range of is the set .

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