Name ______________________________________________
Date __________________________________
Thurgood Marshall Academy Public Charter High School – Pre-Calculus
Notes #11 – Function Notation for Ordered Pairs
Topic: General Properties of Functions
Objectives:

11.1 Given a two-variable equation, answer questions about its solutions posed in function notation.
Standards:
A.

A-REI.10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the
coordinate plane, often forming a curve (which could be a line).

F-IF.1. Understand that a function from one set (called the domain) to another set (called the range) assigns to
each element of the domain exactly one element of the range. If f is a function and x is an element of its domain,
then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

F-IF.2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use
function notation in terms of a context.
Is each of the following relations a function? Yes or no.
{(5,2), (−3, 8), (3, −8), (5, 4)}
{(3,2), (4,2), (5, 2), (−3, 2)}
B.
We often use letters as names for relations. These letters are not _________________________.
Suppose f is the relation whose ordered pairs are the solutions of 𝑦 = 2𝑥 − 3. Name three ordered pairs
belonging to f.
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C.
“(5, w) is an ordered pair in the relation named g. Find w.”
If g is not a function, then there might be __________________ correct answers to this question.
“(5, w) is an ordered pair in the relation named g. Find w.”
If g is a function, then there is no more than _______________ correct answer to this question:
D.
𝑓(5) = 7 means that the ordered pair ___________ belongs to the function named f.
We can only use this notation if f is a ______________________________. If f is a relation but not a
____________________________, then 𝑓(5) would not necessarily equal one specific number.
E.
Suppose the function named g contains the ordered pairs that satisfy 𝑦 = 2𝑥 − 3.
True or false: 𝑔(4) = 5?
What is 𝑔(−3)?
Find 𝑚 such that 𝑔(𝑚) = −11.
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Practice Exercises #11 – Function Notation for Ordered Pairs
11.1 Given a two-variable equation, answer questions about its solutions posed in function notation.
1.
Suppose g contains the ordered pairs satisfying 𝑥 − 𝑦 = 10. Find 𝑔(−4).
2.
f is the function containing all of the ordered pairs satisfying 𝑦 = −2𝑥 − 3. Find m so that 𝑓(𝑚) = −11.
3.
Suppose the function named g contains the ordered pairs that satisfy 𝑦 = √𝑥 + 2 − 3.
True or false: 𝑔(2) = −1?
What is 𝑔(14)?
Find 𝑎 such that 𝑔(𝑎) = 0.
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4.
Suppose k contains the ordered pairs satisfying 𝑦 = 3𝑥 + 1. Find 𝑘(5).
5.
Suppose m contains the ordered pairs satisfying 𝑦 = −𝑥 + 1. Find w such that 𝑚(𝑤) − 3.
6.
Suppose p contains the ordered pairs satisfying 𝑥 − 𝑦 = 12. Find 𝑝(4).
7.
Suppose p contains the ordered pairs satisfying 𝑥 − 𝑦 = 12. Find x such that 𝑝(𝑥) = −9.
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8.
Suppose f contains the ordered pairs satisfying 𝑦 = 𝑥 3 . Find 𝑓(−3).
9.
Suppose f contains the ordered pairs satisfying 𝑦 = 𝑥 2 + 1. Find 𝑓(−3).
10.
Suppose f contains the ordered pairs satisfying 𝑦 = 𝑥 4 + 𝑥. Find 𝑓(−2).
11.
Suppose f contains the ordered pairs satisfying 𝑦 = 𝑥 2 − 5𝑥 − 9. Find 𝑓(−3).
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12.
Suppose 𝑔 contains the ordered pairs satisfying 𝑥 = √𝑦 + 3. Find x such that 𝑔(𝑥) = 22.
13.
Suppose f contains the ordered pairs satisfying 𝑦 = −(𝑥 + 3)2 . Find 𝑓(−1).
14.
Suppose g contains the ordered pairs satisfying 𝑦 = |𝑥 2 + 2𝑥 + 1|. Find 𝑓(−5).
15.
Suppose f contains the ordered pairs satisfying 𝑦 = 4 𝑥 + 2. Find 𝑓(12).
3
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3
16.
Suppose f contains the ordered pairs satisfying 𝑥 = − 5 𝑦 − 11. Find m such that 𝑓(𝑚) = 20.
17.
Suppose f contains the ordered pairs satisfying 𝑦 = 𝑥 + 2. Find m such that 𝑓(𝑚) = 20.
18.
Suppose f contains the ordered pairs satisfying 𝑥 = − 5 𝑦 − 11. Find 𝑓(10).
3
4
3
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19.
Suppose f contains the ordered pairs satisfying 𝑦 =
2𝑥+1
.
3
20.
Suppose h contains the ordered pairs satisfying 𝑥 =
3𝑦−1
.
2
3
Find 𝑓 (2).
2
Find n such that 𝑓(𝑛) = 3.
ANSWERS
1. -14
2. 4
3. True, 1, 7
4. 16
5. 4
6. -8
7. 3
8. -27
9. 10
10. 14
11. 15
12. 5
13. -4
14. 16
15. 11
16. -33
17. 24
18. -35
19. 4/3
20. 1/2
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