Free Printable Functions

1.

Indicate all the diagrams that are functions.

a)

b)

c)

d)

e)

2.

What statements are correct for a function?

a)

A function has only one input

b)

An input can have different output

c)

A function map one input to only one output

d)

All input has an output

e)

Input is an element in Domain and output is an element in Co-domain

3.

Which statement is correct about the diagram.

a)

It is a relation, but not a function because there is a negative number in the domain

b)

It is neither relation nor a function

c)

It is a relation and a function

d)

It is a relation, but not a function because 11 has two outputs

e)

It is a not relation, but a function

4.

Which set of values are a function?

a)

{(9,5),(10,5), (9,-5), (10,-5)}

b)

{(3,4), (4,-3), (7,4), (3, 8)}

c)

{(6,-5), (7, -3),(8, -1), (9, 1)}

d)

{(2, -2), (5, 9), (5, -7), (1, 4)}

e)

{(6,-5), (7, -3), (8, -1), (9, 1), (6,-1)}

5.

Which graphs are functions?

a)

b)

c)

d)

e)

6.

Define functions f and g from R to R by the following
formulas: For every x in R, $f(x)\ =\ 2x$ and $g(x)\ =\ \frac{2x^3+2x}{x^2+1}$ . Which statement is correct?

a)

$f\left(x\right)=g\left(x\right)$ because the domain and co-domain are euqal

b)

$f\left(x\right)\ne g\left(x\right)$ because the domain are not equal

c)

$f\left(x\right)\ne g\left(x\right)$ because the the co-domain are not equal

d)

$f\left(x\right)=g\left(x\right)$ because for every x, f(x) = g(x)

7.

Define a function f : Z+ -> Z+ as follows: For

each positive integer n, f(n) = the sum of all of the positive divisors of n. What is f(15)?

a)

1

b)

3

c)

5

d)

15

e)

24

8.

Define a boolean function f: {0,1} -> {0,1}, f(x,y,z) = (2x-y+z) mod 2. What is f(2,6,1)?

a)

-1

b)

0

c)

1

d)

Undefined

9.

Consider F. Which statements are correct?

a)

F is one-to-one

b)

F is onto

c)

F is not a function

d)

None of the answers

10.

Consider H. Which statement is true?

a)

H is one-to-one

b)

H is onto

c)

H is not a function

d)

None of the answers

11.

Define f : R -> R, f(n) = 4n + 5. Which statements are correct?

a)

f is one-to-one

b)

f is onto

c)

f is not a function

d)

None of the answers

12.

Define f : Z -> Z, $f\left(x\right)\ =\ x^2+1$ . Which statements are correct?

a)

f is one-to-one

b)

f is onto

c)

f is not a function

d)

None of the answers

13.

Let A = {0, 1} and let S be the set of all strings over A. For all x in S, define f to be from S to N, f(x) = the length of x. Which statements are correct? (N is a natural number set)

a)

f is one-to-one

b)

f is onto

c)

f is not a function

d)

None of the answers

14.

Define f: R -> Z, $f\left(x\right)\ =\ \lceil x\rceil$ . Which statements are correct? ( $\lceil x\rceil$ is a ceiling of x)

a)

f is one-to-one

b)

f is onto

c)

f is not a function

d)

None of the answers

15.

Which of the following functions has an inverse?

a)

f: R-> R, f(x) = x+2

b)

f: Z-> Z, f(x) = x+2

c)

f: R+-> R+, f(x) = |x|

d)

f: R-> R, $f\left(x\right)\ =\ x^2$

e)

f: R-> N, $f\left(x\right)\ =\ \lceil x\rceil$

16.

Define f : R -> R and g : R -> Z by the following
formulas: $f\left(x\right)\ =\ \frac{x^2}{3}$ and $g\left(x\right)\ =\ \lfloor x\rfloor$ ; for every x in R. What is gof(2)?

a)

-1

b)

0

c)

1

d)

2

17.

Define f : R -> R and g : R -> R. Let f(x) = 3x and g(x) = $\lceil\frac{x}{3}\rceil$ for every real number x. What is fog (5)?

a)

3

b)

5

c)

6

d)

8

e)

0

18.

Let f(x) = x^5 and g(x)^5 = x^(1/5) for each real number x. Find f o g (5)

a)

0

b)

1

c)

5

d)

10

19.

Define f: R X R -> R X R as follows: f(x, y) = (x+1, 2-y) for every (x, y) in R X R. Is H one-to-one and/or onto?

a)

neither

b)

one-to-one but not onto

c)

not one-to-one but onto

d)

both one-to-one and onto

20.

The Hamming distance function. Let Sn be the set of all strings of 0’s and 1’s of length n. Define a function H : Sn X Sn -> N (natural number set) as follows: For each pair of strings (s,t) in Sn X Sn, H(s,t) = the number of positions in which s and t have different values. Find H(00110, 10111).

a)

1

b)

2

c)

3

d)

5

21.

The Hamming distance function. Let Sn be the set of all strings of 0’s and 1’s of length n. Define a function H : Sn X Sn -> N (natural number set) as follows: For each pair of strings (s,t) in Sn X Sn, H(s,t) = the number of positions in which s and t have different values. Determine if H is one-to-one or onto?

a)

Neither

b)

one-to-one but not onto

c)

Not one-to-one, but onto

d)

Both one-to-one and onto

Functions

Total questions: 21

Worksheet time: 20mins

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