What is a Function?
A table of values or set of ordered pairs is a function if _________________________________
Do these tables and ordered pairs represent a function? Explain.
x
f(x)
2
0
5
1
3
9
6
5
{ (0,2) (1,4) (5,3), (8,3)}
x
4
3
4
2
f(x)
7
6
5
4
{(1,1) (2,2) (3,3) (2,5) (4,4) (6,1) }
A graph is a function if _________________________________
Do these graphs represent a function? Explain.
y
y
x
x
Functions WS A
Name___________________
Determine if the following graphs are functions. Explain why or why not.
1.
Function:
Function:
Yes /No
Function:
Yes /No
Yes /No
Function:
Yes /No
Determine if the following ordered pairs are functions. Explain why or why not.
2.
(5,1); (4,6); (9,-5); (1,-5)
(8,-3); (10,4); (-6,-3); (-6,8)
Function:
Function:
Yes/No
Yes/No
(1,-2); (-2,1); (3,4); (4,3)
(1,-2); (2,-2); (3,-2); (4,-2)
Function:
Function:
Yes/No
Yes/No
3. Determine if the following tables are functions. Explain why or why not.
x
f(x)
x
f(x)
x
f(x)
-8
-5
-8
5
1
-5
-5
-3
-2
5
1
-3
-1
-1
-1
5
2
-1
0
1
0
5
2
1
1
3
2
5
1
3
Function:
Yes /No
x
f(x)
-6
-3
-5
-2
-4
-1
1
0
2
1
Function:
Yes /No
Function:
Yes /No
Function:
Yes /No
Discrete Functions
Discrete function:
Set notation:
Domain:
Range:
1. (1,-2); (-2,1); (3,4); (4,3)
2.
3.
x
f(x)
-8
-5
-5
-3
-1
-1
0
1
1
3
Functions WS B
Name___________________
Label each point with the correct coordinate. Then, state the domain and range.
1.
Domain:
Range:
2.
Domain:
Range:
3.
Domain:
Range:
State the domain and range for each discrete function.
4.
6.
(5,1); (4,6); (9,-5); (1,-5)
5. (1,-2); (2,-2); (3,-2); (4,-2)
Domain:
Domain:
Range:
Range:
x
f(x)
-8
7.
x
f(x)
-5
-6
4
-5
-3
-5
4
-1
-1
-4
4
0
1
1
4
1
3
2
4
Domain:
Domain:
Range:
Range:
Continuous Functions
Continuous function:
Functions WS C
Name___________________
Find the domain and range of the following situations.
1.
Domain:
Range:
2.
Domain:
Range:
3.
Domain:
Range:
4.
Domain:
Range:
5.
Domain:
Range:
6.
Domain:
Range:
Name__________________________
1.
2.
3.
4.
5.
6.
7.
8.
Functions WS D
Name___________________
For each function below state if the function is discrete or continuous. Then, state the domain and range.
y
1.
2.





x














3.
4.

X
f(x)
2
7
6
5
4
0
3
1



   










5. (0, 4) (2, 5) (3, 5) (4, 8)
6. (2, 0) (5, 9) (4, 2) (8, 6) (3, 3)
7.
8.




   





9.






Functions WS E
Name___________________
Use graphs A-L from the additional sheet to answer the questions below. Use all letters in each question
1. Determine which graphs are functions and which graphs are not functions. Write the corresponding letter from the
graphs.
Function
Not a Function
2. Determine which graphs are discrete and which graphs are continuous. Write the corresponding letter from the
graphs.
Discrete
Continuous
3. Analyze each graph from left to right. Determine if the graphs are increasing, decreasing, both increasing and
decreasing, or neither increasing nor decreasing. Write the corresponding letters from the graphs.
Increasing
Decreasing
Neither
4. Determine whether the graphs are linear or non-linear. Write the corresponding letters from the graphs.
Linear
Non-linear
Function Definitions Quiz
Name____________________
For each graph below, circle all that apply.
Function
Not a Function
Discrete
Continuous
Linear
Non-linear
Increasing
Decreasing
1.
Neither
Function
Not a Function
Discrete
Continuous
Linear
Non-linear
Increasing
Decreasing
2.
3.
4.
Function
Not a Function
Discrete
Continuous
Linear
Non-linear
Increasing
Decreasing
Function
Not a Function
Discrete
Continuous
Linear
Non-linear
Increasing
Decreasing
Neither
Neither
Neither
For each of the following:
a) Determine if it is a function. EXPLAIN!
b) Discrete or continuous
c) State the domain and range
5.
6.
a)__________________________________
a)__________________________________
_________________________________
_________________________________
b) _________________________________
b) _________________________________
c)__________________________________
c)__________________________________
7.
x
f(x)
3
4
9
8
3
7
4
18
8.
(1,1) (2, 1) (3, 5) (4, 3)
a)__________________________________
_________________________________
a)__________________________________
_________________________________
b) _________________________________
c)__________________________________
b) _________________________________
c)__________________________________
Function Definitions Quiz
Name____________________
For each graph below, circle all that apply.
Function
Not a Function
Discrete
Continuous
Linear
Non-linear
Increasing
Decreasing
1.
Function
Not a Function
Discrete
Continuous
Linear
Non-linear
Increasing
Decreasing
Neither
2.
3.
4.
Function
Not a Function
Discrete
Continuous
Linear
Non-linear
Increasing
Decreasing
Function
Not a Function
Discrete
Continuous
Linear
Non-linear
Increasing
Decreasing
Neither
Neither
Neither
For each of the following:
a) Determine if it is a function. EXPLAIN!
b) Discrete or continuous
c) State the domain and range
5.
6.
a)__________________________________
a)__________________________________
_________________________________
_________________________________
b) _________________________________
b) _________________________________
c)__________________________________
c)__________________________________
7.
x
f(x)
1
1
2
1
3
5
4
3
a)__________________________________
_________________________________
b) _________________________________
c)__________________________________
8.
(3, 4) (9, 8) (3, 7) (4, 18)
a)__________________________________
_________________________________
b) _________________________________
c)__________________________________
Function Notation
f(x) = _____
Ordered pair:
Input:
Output:
Using the function f(x) = -2x + 6:
Input:
Output:
How to find f(4):
Use the function to complete each problem. Write your answer in function notation and as an ordered pair.
1. 𝑓(𝑥) = 3𝑥 + 5)
a) 𝑥 = 2
b) 𝑥 = −5
2. 𝑔(𝑥) = −8(𝑥 + 2)
a) 𝑥 = −2
b) 𝑥 = 5
3. 𝑘(𝑥) = 2𝑥 2
a) 𝑘(3)
b) 𝑘(−4)
Functions WS F
Name: _____________________
Determine the output value of each function for the given input values. Write it in function notation and as
an ordered pair.
1. The function is f(x) = 4x with an input of x = 3.
2. The function is g(x) = x4 with an input of x = -2.
3. The function is h(x) = 2x + 7 with an input of x = 4.
4. The function is m(x) = -8x – 4 with an input of x = -9.
Use the given function to complete each problem. Write each solution in function notation and as an
ordered pair.
5. f(x) = x + 8
a) 𝑥 = −3
b) 𝑥 = 2
6. g(x) = 2x – 7
a) 𝑥 = 0
b) 𝑥 = −1
7. b(x) = x2 + 2
a) 𝑥 = 5
b) 𝑥 = −4
Functions WS G
Name: _____________________
Use the function to complete each problem. Write your answer in function notation and as an ordered pair.
1. 𝑓(𝑥) = 3(𝑥 − 8)
a) 𝑥 = 2
b) 𝑥 = −3
2. 𝑔(𝑥) = 6𝑥 − 12
a) 𝑥 = −1
b) 𝑥 = 7
3. 𝑘(𝑥) = 3𝑥 2
a) 𝑥 = 7
b) 𝑥 = −4
4. 𝑔(𝑥) = 4 − 3(𝑥 + 1)
a) 𝑥 = −6
b) 𝑥 = 2
5. 𝑚(𝑥) = 8𝑥 + 2
a) 𝑥 = −3
b) 𝑥 = 4
6. ℎ(𝑥) = 7𝑥
a) 𝑥 = −3
b) 𝑥 = 5
7. 𝑓(𝑥) = 3𝑥 − 4
a) 𝑓(2)
b) 𝑓(−4)
8. 𝑔(𝑥) = 𝑥 2 − 5
a) 𝑔(5)
b) 𝑔(−5)
9. ℎ(𝑥) = −7𝑥 + 8
a) ℎ(2)
b) ℎ(−4)
10. 𝑘(𝑥) = 4 − 3(𝑥 + 1)
a) 𝑘(3)
b) 𝑘(−6)
11. 𝑚(𝑥) = 7 − 3𝑥
a) 𝑚(2)
b) 𝑚(−9)
12. 𝑓(𝑥) = −4𝑥 2
a) 𝑓(2)
b) 𝑓(−4)
Functions as Tables and Graphs
Example: Complete the table for g(x) = 4x – 11.
x
2
5
7
9
f(x)
Use the table above to answer:
a) 𝑓(5) = _________
b) 𝑓(_________) = 17
Example: The function, w(d) on the right represents the total
number of bottles drank after each of 10 days.
a) What does w(1) = 2 mean?
b) w(8) = ____
c) w(5) = ____
d) w(d) = 8
e) w(d) = 11
Why is w(d) a function?
c) 𝑓(2) = ________
Functions WS H
Name: _____________________
Use the function to complete the table.
1. f(x) = 5x – 3
x
2.
g(x) = 7(x - 2) + 6
x
f(x)
8
-3
2
0
-1
4
-4
10
3. g(x) = 2x – 11
x
0
-3
-5
8
g(x)
4. f ( x)  2  4( x  7)
x
f(x)
-4
-1
3
4
7
g(x)
Complete the tables using the following functions. Then use the table to determine the missing inputs and
outputs.
5. 𝑔(𝑥) = 3𝑥 − 5
x
-7
-2
3
a. 𝑔(3) =______
8
g(x)
b. 𝑔(_______) = 19
6. 𝑓(𝑥) = −6𝑥 − 4
x
-6
-2
1
4
7
f(x)
a. 𝑓(−2) =______
b. 𝑓(_______) = −10
7. ℎ(𝑥) = 3(𝑥 − 7) + 12
x
h(x)
-5
-2
3
8
12
a. ℎ(−2) =______
b. ℎ(_______) = 15
Functions WS I
Name: _____________________
1. The graph on the right shows the number of hours (h) that Stacy spent studying each day (d) for 2 weeks
before her big Calculus test. The graph is represented by the function h(d). Use the graph to find each of
the following.
Study Time
a) h(1) = _____
b) h(8) = _____
c) h(d) = 11, d = _____
Hours
Spent
Studying
d) h(d) = 20, d = _____
Days
2. Use the graph to find each of the following. Write your
answer as an ordered pair.
a) f(2) =
b) f(-1) =
c) f(x)=5, x=
d) f(x)=-2, x=
3. Use the graph to find each of the following. Write your answer as
an ordered pair.
a) f(1)
b)
f(x)=0
c) f(-2)
d) f(x)=2
4. The function m(x) represents the distance Michelle is from her house as she walks her dog. Use the graph
to find each of the following. Write answers as an ordered pair.
a) If x=2, then m(x) = ??
b) If x=7, then m(x) = ??
c) If m(x) = 3, then x = ??
d) If m(x) = 0, then x = ??
5. Use the graph of f(x) below to find each of the following. Write your answer as an ordered pair.
a)
f(2)
b) f(8)
c) f(x) = 4
d) f(x) = -2
e) f(7)
6. Use the graph on the right to find each of the following. Write your solutions as an ordered pair.
a) f(4)
b) f(-1)
c) f(x)=4
d) f(x)=2