Advanced Geometry : How to graph an exponential function

Study concepts, example questions & explanations for Advanced Geometry

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Example Questions

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Example Question #41 : Coordinate Geometry

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

Possible Answers:

Correct answer:

Explanation:

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 #132 : Advanced Geometry

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

Possible Answers:

The graph of  has no -intercept.

Correct answer:

Explanation:

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 #42 : 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.

Explanation:

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:

Explanation:

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 #51 : Coordinate Geometry

Give the domain of the function .

Possible Answers:

The set of all real numbers

Correct answer:

The set of all real numbers

Explanation:

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 #21 : How To Graph An Exponential Function

Give the range of the function .

Possible Answers:

The set of all real numbers

Correct answer:

Explanation:

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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