Precalculus : Algebra of Functions

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #1 : Add, Subtract, Multiply, And Divide Functions

Simplify the following expression: 

Possible Answers:

No correct answer listed

Correct answer:

Explanation:

To simplify the above expression, we must combine all like terms:

Integers: 

 

Putting all of the above terms together, we simplify to:

Example Question #12 : Algebra Of Functions

If  and , what is ?

Possible Answers:

Correct answer:

Explanation:

Given the information in the above problem, we know that:

Factoring the resulting fraction, we get:

Example Question #13 : Algebra Of Functions

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

To simplify the expression, distribute the negative into the second parentheses, and then combine like terms.

Example Question #14 : Algebra Of Functions

Simplify the following completely:

Possible Answers:

Correct answer:

Explanation:

To simlify adding polynomials, simply drop the parentheses and add like terms.

Example Question #15 : Algebra Of Functions

Determine the sum of:  

Possible Answers:

Correct answer:

Explanation:

To add the numerators, the denominators must be common.

The least common denominator can be determined by multiplication.

Rewrite the fractions.

Example Question #16 : Algebra Of Functions

Given  and ,

Complete the operation given by .

Possible Answers:

Correct answer:

Explanation:

Given  and 

Complete the operation given by .

Begin by realizing what this is asking. We need to combine our two functions in such a way that we find the difference between them.

When doing so remember to distribute the negative sign that is in front of  to each term within the polynomial.

So, by simplifying the expression, we get our answer to be:

Example Question #17 : Algebra Of Functions

Given  and ,

Evaluate and simplify .

Possible Answers:

Correct answer:

Explanation:

Given  and ,

Evaluate and simplify .

Begin by multiplying  by 2:

Next, add  to what we got above and combine like terms.

This makes our answer 

.

 

Example Question #18 : Algebra Of Functions

Given  and , find .

Possible Answers:

Correct answer:

Explanation:

Given  and , find .

To complete this problem, we need to recall FOIL. FOIL states to multiply the terms in each binomial together in the order of first, outer, inner, and last.

We have no like terms to combine, so our answer is:

Example Question #19 : Algebra Of Functions

Determine 

if 

  and 

Possible Answers:

Correct answer:

Explanation:

 is defined as the sum of the two functions  and .

As such

 

Example Question #20 : Algebra Of Functions

Determine 

if 

  and 

Possible Answers:

Correct answer:

Explanation:

 is defined as the sum of the two functions  and .

As such

 

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