Precalculus : Functions

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #53 : Pre Calculus

What is the domain of the following function?

Possible Answers:

-

Correct answer:

Explanation:

The denominator becomes zero whenever cos(x) becomes -1 and this happens when x is an odd multiple of .  To avoid division by zero, we exclude all these numbers. Therefore the domain is:

 

Example Question #1 : Algebra Of Functions

Simplify the following expression:

Possible Answers:

Correct answer:

Explanation:

When multiplying polynomials, add their exponents.

Example Question #22 : Functions

Simplify this polynomial:

Possible Answers:

Correct answer:

Explanation:

When dividing polynomials, you must subtract corresponding exponents.

Thus, our answer is

.

Example Question #23 : Functions

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

When dividing, we must subtract the exponents.

Thus, our answer is  .

Example Question #1 : Piecewise Functions

Let

What does  equal when ?

Possible Answers:

Correct answer:

Explanation:

Because 3>0 we plug the x value into the bottom equation.

Example Question #2 : Piecewise Functions

Let

What does  equal when ?

Possible Answers:

Correct answer:

Explanation:

Because  we use the first equation.

Therefore, plugging in x=0 into the above equation we get the following,

.

Example Question #26 : Functions

Determine the value of  if the function is

Possible Answers:

Correct answer:

Explanation:

In order to determine the value of  of the function we set  

The value comes from the function in the first row of the piecewise function, and as such

Example Question #1 : Piecewise Functions

Determine the value of  if the function is



Possible Answers:

Correct answer:

Explanation:

In order to determine the value of  of the function we set  

The value comes from the function in the first row of the piecewise function, and as such

Example Question #28 : Functions

For the function  defined below, what is the value of  when ?

Possible Answers:

8

0

-2

7

3

Correct answer:

8

Explanation:

Evaluate the function for . Based on the domains of the three given expressions, you would use , since  is greater than or equal to .

Example Question #29 : Functions

If  is the greatest integer function, what is the value of 

Possible Answers:

Correct answer:

Explanation:

The greatest integer function takes an input and produces the greatest integer less than the input. Thus, the output is always smaller than the input and is an integer itself. Since our input was , we are looking for an integer less than this, which must be  since any smaller integer would by definition not be "greatest". 

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