Precalculus : Functions

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #61 : Functions

Find the domain of the function:

Possible Answers:

Correct answer:

Explanation:

The square cannot house any negative term or can the denominator be zero. So the lower limit is  since  cannot be , but any value greater than it is ok. And the upper limit is infinity.

Example Question #62 : Functions

What is the domain for the function?

Possible Answers:

Correct answer:

Explanation:

 The denominator becomes  when  or , so the function does not exist at these points. In numerator,  must be at least   or greater to be real. So the function is continuous from  to  and  to any other value greater than .

Example Question #63 : Functions

What is the domain of the function below?

Possible Answers:

Correct answer:

Explanation:

The denomiator factors out to:

The denominator becomes zero when . But the function can exist at any other value.

Example Question #64 : Functions

What is the domain of the function below?

Possible Answers:

Correct answer:

Explanation:

Cannot have a negative inside the square root. The value of  has to be  for the inside of the square root to be at least . This is the lower bound of the domain. Any value of  greater than  exists.

Example Question #65 : Functions

Possible Answers:

Correct answer:

Explanation:

The natural log function does not exist if the inside value is negatuve or zero. The points where the inside becomes negative are  or . If  is greater than , both terms,  and , are positive. If  is less than , both terms are negative and multiply to become positive. If the  value is between  and , only one term will be negative and result in a , which does not exist.

Example Question #1196 : Pre Calculus

What is the domain of the function?

Possible Answers:

Correct answer:

Explanation:

The value inside a natural log function cannot be negative or . At , the inside is  and any  value less than  cannot be included, because result will be a negative number inside the natural log. 

Example Question #67 : Functions

What is the domain of the function?

Possible Answers:

Does not exist anywhere.

Correct answer:

Explanation:

Exponentials cannot have negatives on the inside. However, the expoential will convert any  value into a positive value.

Example Question #66 : Functions

What is the domain of the function?

Possible Answers:

Correct answer:

Explanation:

Looking at the denominator, the function cannot exist at . The natural log function cannot have a  or negative inside. Since the  value is raised to the power of , any negative  value will be convert to a positive value. However, the function will not exist if the inside of the natural is , where .  will exist any where else.

Example Question #67 : Functions

What is the domain of the function?

Possible Answers:

Correct answer:

Explanation:

The denominator becomes  where , and the inside of the natural log also becomes  at . The function will not exist at these two points.  The  value cannot be less than , becuase that will leave a negative value inside in the natural log.

Example Question #1203 : Pre Calculus

Find the domain of the function.

Possible Answers:

Correct answer:

Explanation:

Simplify:

 

Even though the  cancels out from the numerator and denominator, there is still a hole where the function discontinues at . The function also does not exist at , where the denominator becomes

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