# Algebra 1 : Algebraic Functions

## Example Questions

Explanation:

### Example Question #11 : How To Find F(X)

An infinite sequence begins as follows:

Assuming this pattern continues infinitely, what is the sum of the first one hundred terms?

Explanation:

This can be best solved by looking at this sum as follows:

with  taken as an addend fifty times. This is equal to

### Example Question #13 : Algebraic Functions

Define . Which function is equal to  ?

Explanation:

Define  and  .

What is  ?

Explanation:

Define  and

What is  ?

Explanation:

### Example Question #11 : How To Find F(X)

Each of the four tables below defines a relationship between  (domain) and  (range).

One of these tables does not define a function.  Identified the table.

None of the above.

Table 1

Table 4

Table 3

Table 2

Table 3

Explanation:

In table 3 we see an  value of 3 gets tranformed into 5, 7, 9 ,and 11 which is not possible for a function.  Hence the relationship between  and  in Table 3 does not define a function.

### Example Question #17 : Algebraic Functions

Each of the following 4 sets defines a relationship between  and .  Which of these four sets defines a one-to-one function:

A =

B=

C =

D =

Set A and Set B

Set C

Set B

Set A

Set D

Set A

Explanation:

Only in set A one can see that there is an unique value of  for each value of  and similarly each of the  values maps into one and only one  value.  Hence set A must define a one-to-one function.

### Example Question #61 : Functions And Lines

Which of the following equations does not represent a function?

Explanation:

The correct answer is equation D.  If we solve for  we get

The fact that each value of  gives us two values of   disqualifies it as a function.

### Example Question #19 : Algebraic Functions

Which of the following equations represents a one-to-one function:

Explanation:

Only equation B maps each value of  into a unique value of  and in a similar way each and every value of  maps into one and only one value of .

### Example Question #20 : Algebraic Functions

Test whether the given function is symmetric with respect to the -axis, -axis, origin.

x axis

y axis

origin

All of the above

Not symmetric with respect to x axis, y axis, and the origin

Not symmetric with respect to x axis, y axis, and the origin

Explanation:

Since

It is not symmetric with respect the -axis

It is not symmetric with respect to the -axis

Hence multiplying by  both sides we get

Hence it is not symmetric with respect to the origin.