Precalculus : Functions

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #1 : Absolute Value Functions

Which of the following is a point on the following function?

 

Possible Answers:

Correct answer:

Explanation:

One way to approach this problem would be to plug in each answer and see what works. However, I would be a little more strategic and eliminate any options that don't make sense.

Our y value will never be negative, so eliminate any options with a negative y-value.

Try (0,0) really quick, since it's really easy

The only point that makes sense is (5,83), therefore it is the correct answer

Example Question #31 : Functions

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

Cancel the absolute value sign by separating the function  into its positive and negative counterparts.

Evaluate the first scenario.

Evaluate the second scenario.

The correct answer is:

Example Question #33 : Functions

If   , then what is the value of  when  ?

Possible Answers:

-7

20

13

7

-13

Correct answer:

13

Explanation:

We evaluate for 

Since the absolute value of any number represents its magnitude from  and is therefore always positive, the final answer would be 

Example Question #34 : Functions

Given  and , evaluate .

Possible Answers:

Correct answer:

Explanation:

We are given two functions and asked to find f(h(7)).

I would begin by finding h(7)

Now that we know h(7), we go ahead and plug it into f(x).

So our final answer is simply 8.

Example Question #35 : Functions

Solve the function.  

Possible Answers:

Correct answer:

Explanation:

Determine the domain of .

Multiply  on both sides of the equation to cancel the denominator and divide the equation  by ten.

Since the domain states that , the only possible answer is .

Example Question #36 : Functions

Solve for :  

Possible Answers:

Correct answer:

Explanation:

Rewrite  so that the exponential variable is isolated.

Reconvert  to a similar base.  Use exponents to redefine the terms.

Since all terms are of the same base, use the property of log to eliminate the base on both sides of the equation.

Solve for .

Example Question #37 : Functions

Evaluate the following function when 

Possible Answers:

Correct answer:

Explanation:

Evaluate the following function when 

To evaluate this function, simply plug-in 6 for t and simplify:

So our answer is:

Example Question #38 : Functions

Determine the value of  of the function

Possible Answers:

Correct answer:

Explanation:

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

As such

Example Question #39 : Functions

Find the difference quotient of the function .

Possible Answers:

Correct answer:

Explanation:

Difference quotient equation is 

 and 

.

Now plug in the appropriate terms into the equation and simplify:

Example Question #40 : Functions

Find the value of the following function when 

Possible Answers:

The function is undefined at 

Correct answer:

The function is undefined at 

Explanation:

Find the value of the following function when 

To evaluate this function, plug in 2 for x everywhere it arises and simplify:

So our answer must be undefined, because we cannot divide by 

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