GMAT Math : Understanding functions

Study concepts, example questions & explanations for GMAT Math

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Example Questions

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Example Question #1 : Understanding Functions

There is water tank already \frac{4}{7} full. If Jose adds 5 gallons of water to the water tank, the tank will be \frac{13}{14} full. How many gallons of water would the water tank hold if it were full?

Possible Answers:

14

25

20

5

15

Correct answer:

14

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 x. According to the question, \frac{4}{7}-full  can be replaced as \frac{4}{7}x\frac{13}{14}-full  would be \frac{13}{14}x. Therefore, we can write out the equation as: 

\frac{4}{7}x+5=\frac{13}{14}x.

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:

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 #3 : Understanding Functions

Let  be a function that assigns x^{2} to each real number .  Which of the following is NOT an appropriate way to define ?

Possible Answers:

y=x^{2}

f(y)=x^{2}

f(x)=x^{2}

all are appropriate ways to define

Correct answer:

f(y)=x^{2}

Explanation:

This is a definition question.  The only choice that does not equal the others is f(y)=x^{2}.  This describes a function that assigns x^{2} to some number , instead of assigning x^{2} to its own square root, .

Example Question #4 : Understanding Functions

If f(x)=x^{2}, find \frac{f(x+h)-f(x)}{h}.

Possible Answers:

x^{2}+4x+4

x^{2}

x^{2}+2xh+h^{2}

Correct answer:

Explanation:

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

f(x+h)=(x+h)^{2}=x^{2}+2xh+h^{2}

Then \frac{f(x+h)-f(x)}{h}= \frac{x^{2}+2xh+h^{2}-x^{2}}{h} = \frac{2xh+h^{2}}{h}=2x+h

Example Question #2 : Understanding Functions

Give the range of the function:

Possible Answers:

Correct answer:

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 #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:

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 #6 : Functions/Series

Give the inverse of

Possible Answers:

Correct answer:

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 #7 : Understanding Functions

Define . Give 

Possible Answers:

Correct answer:

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 #3 : Understanding Functions

Define  and .

Give the definition of  .

Possible Answers:

Correct answer:

Explanation:

Example Question #4 : Understanding Functions

Define  .

If , evaluate .

Possible Answers:

Correct answer:

Explanation:

Solve for  in this equation:

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