### All GMAT Math Resources

## Example Questions

### Example Question #1 : Understanding Functions

There is water tank already full. If Jose adds 5 gallons of water to the water tank, the tank will be full. How many gallons of water would the water tank hold if it were full?

**Possible Answers:**

**Correct answer:**

In this case, we need to solve for the volume of the water tank, so we set the full volume of the water tank as . According to the question, -full can be replaced as . -full would be . Therefore, we can write out the equation as:

.

Then we can solve the equation and find the answer is 14 gallons.

### Example Question #2 : Understanding Functions

There exists a set = {1, 2, 3, 4}. Which of the following defines a function of ?

**Possible Answers:**

none are functions

two are functions

**Correct answer:**

Let's look at and see if any of them are functions.

1. = {(2, 3), (1, 4), (2, 1), (3, 2), (4, 4)}: This cannot be a function of because two of the ordered pairs, (2, 3) and (2, 1) have the same number (2) as the first coordinate.

2. = {(3, 1), (4, 2), (1, 1)}: This cannot be a function of because it contains no ordered pair with first coordinate 2. Because the set = {1, 2, 3, 4}, we need an ordered pair of the form (2, ) .

3. = {(2, 1), (3, 4), (1, 4), (2, 1), (4, 4)}: This is a function. Even though two of the ordered pairs have the same number (2) as the first coordinate, is still a function of because (2, 1) is simply repeated twice, so the two ordered pairs with first coordinate 2 are equal.

### Example Question #3 : Understanding Functions

Let be a function that assigns to each real number . Which of the following is NOT an appropriate way to define ?

**Possible Answers:**

all are appropriate ways to define

**Correct answer:**

This is a definition question. The only choice that does not equal the others is . This describes a function that assigns to some number , instead of assigning to its own square root, .

### Example Question #4 : Understanding Functions

If , find .

**Possible Answers:**

**Correct answer:**

We are given f(x) and h, so the only missing piece is f(x + h).

Then

### Example Question #5 : Understanding Functions

Give the range of the function:

**Possible Answers:**

**Correct answer:**

We look at the range of the function on each of the three parts of the domain. The overall range is the union of these three intervals.

On , takes the values:

or

On , takes the values:

,

or

On , takes only value 5.

The range of is therefore , which simplifies to .

### Example Question #6 : Understanding Functions

A sequence begins as follows:

It is formed the same way that the Fibonacci sequence is formed. What are the next two numbers in the sequence?

**Possible Answers:**

**Correct answer:**

Each term of the Fibonacci sequence is formed by adding the previous two terms. Therefore, do the same to form this sequence:

### Example Question #7 : Understanding Functions

Give the inverse of

**Possible Answers:**

**Correct answer:**

The easiest way to find the inverse of is to replace in the definition with , switch with , and solve for in the new equation.

### Example Question #8 : Understanding Functions

Define . Give

**Possible Answers:**

**Correct answer:**

The easiest way to find the inverse of is to replace in the definition with , switch with , and solve for in the new equation.

### Example Question #9 : Understanding Functions

Define and .

Give the definition of .

**Possible Answers:**

**Correct answer:**

### Example Question #10 : Understanding Functions

Define .

If , evaluate .

**Possible Answers:**

**Correct answer:**

Solve for in this equation: