### All College Algebra Resources

## Example Questions

### Example Question #1 : Miscellaneous Functions

Define a function .

Which statement correctly gives ?

**Possible Answers:**

**Correct answer:**

The inverse function of a function can be found as follows:

Replace with :

Switch the positions of and :

or

Solve for . This can be done as follows:

Square both sides:

Add 9 to both sides:

Multiply both sides by , distributing on the right:

Replace with :

### Example Question #1 : Miscellaneous Functions

Refer to the above diagram, which shows the graph of a function .

True or false: .

**Possible Answers:**

False

True

**Correct answer:**

False

The statement is false. Look for the point on the graph of with -coordinate by going right unit, then moving up and noting the -value, as follows:

, so the statement is false.

### Example Question #3 : Miscellaneous Functions

The above diagram shows the graph of function on the coordinate axes. True or false: The -intercept of the graph is

**Possible Answers:**

False

True

**Correct answer:**

False

The -intercept of the graph of a function is the point at which it intersects the -axis (the vertical axis). That point is marked on the diagram below:

The point is about one and three-fourths units above the origin, making the coordinates of the -intercept .

### Example Question #4 : Miscellaneous Functions

A function is defined on the domain according to the above table.

Define a function . Which of the following values is *not* in the range of the function ?

**Possible Answers:**

**Correct answer:**

This is the composition of two functions. By definition, . To find the range of , we need to find the values of this function for each value in the domain of . Since , this is equivalent to evaluating for each value in the range of , as follows:

Range value: 3

Range value: 5

Range value: 8

Range value: 13

Range value: 21

The range of on the set of range values of - and consequently, the range of - is the set . Of the five choices, only 45 does not appear in this set; this is the correct choice.

### Example Question #5 : Miscellaneous Functions

Evaluate:

**Possible Answers:**

**Correct answer:**

Evaluate the expression for , then add the four numbers:

### Example Question #6 : Miscellaneous Functions

Evaluate:

**Possible Answers:**

**Correct answer:**

Evaluate the expression for , then add the five numbers:

### Example Question #1 : Miscellaneous Functions

refers to the *floor* of , the greatest integer less than or equal to .

refers to the *ceiling* of , the least integer greater than or equal to .

Define and

Which of the following is equal to ?

**Possible Answers:**

**Correct answer:**

, so, first, evaluate by substitution:

, so evaluate by substitution.

,

the correct response.

### Example Question #8 : Miscellaneous Functions

refers to the *floor* of , the greatest integer less than or equal to .

refers to the *ceiling* of , the least integer greater than or equal to .

Define and .

Evaluate

**Possible Answers:**

**Correct answer:**

, so first, evaluate using substitution:

, so evaluate using substitution:

,

the correct response.

### Example Question #9 : Miscellaneous Functions

Consider the polynomial

,

where is a real constant. For to be a zero of this polynomial, what must be?

**Possible Answers:**

None of the other choices gives the correct response.

**Correct answer:**

By the Factor Theorem, is a zero of a polynomial if and only if . Here, , so evaluate the polynomial, in terms of , for by substituting 2 for :

Set this equal to 0: