GMAT Math : Understanding functions

Example Questions

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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?

Explanation:

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 #1 : Understanding Functions

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

none are functions

two are functions

Explanation:

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 #1221 : Gmat Quantitative Reasoning

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

all are appropriate ways to define

Explanation:

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 #1 : Understanding Functions

If , find .

Explanation:

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:

Explanation:

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 #1231 : Gmat Quantitative Reasoning

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?

Explanation:

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

Explanation:

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 #1232 : Gmat Quantitative Reasoning

Define . Give

Explanation:

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  .

Explanation:

Define  .

If , evaluate .