College Algebra : Graphs

Study concepts, example questions & explanations for College Algebra

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Example Questions

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Example Question #1 : Miscellaneous Functions

Evaluate: 

Possible Answers:

Correct answer:

Explanation:

Evaluate the expression  for , then add the four numbers:

 

Example Question #1 : Miscellaneous Functions

Evaluate: 

Possible Answers:

Correct answer:

Explanation:

Evaluate the expression  for , then add the five numbers:

Example Question #1 : Miscellaneous Functions

refers to the floor of , the greatest integer less than or equal to .

refers to the ceiling of , the least integer greater than or equal to .

Define and

Which of the following is equal to ?

Possible Answers:

Correct answer:

Explanation:

, so, first, evaluate  by substitution:

, so evaluate by substitution.

,

the correct response.

Example Question #1 : Miscellaneous Functions

refers to the floor of , the greatest integer less than or equal to .

refers to the ceiling of , the least integer greater than or equal to .

Define and .

Evaluate

Possible Answers:

Correct answer:

Explanation:

, so first, evaluate using substitution:

, so evaluate using substitution:

,

the correct response.

Example Question #1 : Miscellaneous Functions

Consider the polynomial

,

where  is a real constant. For  to be a zero of this polynomial, what must  be?

Possible Answers:

None of the other choices gives the correct response.

Correct answer:

Explanation:

By the Factor Theorem,  is a zero of a polynomial  if and only if . Here, , so evaluate the polynomial, in terms of , for  by substituting 2 for :

Set this equal to 0:

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