Precalculus : Functions

Study concepts, example questions & explanations for Precalculus

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1811 : High School Math

Let ABC be a right triangle with sides  = 3 inches,  = 4 inches, and  = 5 inches. In degrees, what is the  where  is the angle opposite of side ?

Possible Answers:

Correct answer:

Explanation:

3-4-5_triangle

We are looking for . Remember the definition of  in a right triangle is the length of the opposite side divided by the length of the hypotenuse. 

So therefore, without figuring out  we can find

Example Question #11 : Functions

Simplify the function below:

 

 

Possible Answers:

Correct answer:

Explanation:

We need to use the following formulas:

 

a) 

and

b)

 

We can simplify as follows:

 

Example Question #1 : Using Pythagorean Identities

Simplify

Possible Answers:

Correct answer:

Explanation:

.  Thus: 

Example Question #41 : Pre Calculus

Simplify

Possible Answers:

Correct answer:

Explanation:

 

and

 .

Example Question #2 : Solving Trigonometric Equations

If  , find the value of the function .

Possible Answers:

1

Correct answer:

Explanation:

We can write:

We can also write:

 

 

Now we can substitute the values of (sinx - cosx) and (sinx * cosx) in the obtained function:

 

Example Question #16 : Functions

Identifying a function.

Which of the following is a function.

Possible Answers:

Correct answer:

Explanation:

The only relation listed that doesn't map more than one dependent variable value for some independent variable value is h(x).  Another way of saying this is that each value in the domain of h corresponds to a distinct value in its range.  h(x) is the only one-to-one relation, and so is the only option that is a function.

Example Question #17 : Functions

Evaluating a function.

Evaluate , when

.

Possible Answers:

Correct answer:

Explanation:

Plug in -3 for x in the function rule:

.

Example Question #11 : Functions

Finding inverse functions.

Given,

 

find

.

Possible Answers:

Correct answer:

Explanation:

To find an inversefunction find the input in terms of the output.  In other words, solve the function for the dependent variable.

First, set h(x) = y.  Now solve for y.

Multiply the denominator on both sides

Distribute y

Rearrange to get only x terms on one side.

Factor out x on the left side.

Divide by (y-5) on both sides to get x by itself.

The final step is to recognize that the independent variable is now the dependent variable.  To put this into proper notation switch x and y.  The inverse function is

.

 

 

Example Question #51 : Pre Calculus

Finding an inverse function.

Given


 

find

 

.

Possible Answers:

.

Correct answer:

.

Explanation:

Finding an inverse function is essentially finding the output in terms of the input.  To do this switch the independent and dependent variables.  First set

.

Then

Now, to switch the role of the variables solve for x in terms of y.

or

So, y is now the independent variable, and x is the dependent variable.  The final step is to write the inverse function in proper notation. 

Set  , and .

This gives

.

 

 

 

Example Question #52 : Pre Calculus

Which function below correctly translates  four units to the right and two units down?

Possible Answers:

Correct answer:

Explanation:

The translation  moves the graph of   units to the left if .  To see this, compare the graphs of  and .  A translation to the right must be in the form  if .

A vertical translation is up if .  We want to move the function down, so our translation subtracts two from .

Combining these, we get .

Learning Tools by Varsity Tutors