M3 L11
Lesson 11: The Graph of a Function
Set builder notation for this statement could be written as
Graph { (x, 2x+3)│x is an integer, 2 ≤ x ≤ 8} or
Graph f ={ (x, 2x +3)│x is an integer, 2 ≤ x ≤ 8} b.
What is the domain of this function? c.
What is the range of this function? d.
What is this the set of this function listed as ordered pairs? e.
Graph the function on graph provided. f.
Is this a discrete or continuous graph?
a.
What is the difference between this instruction and the instruction in example 1? b.
Write this instruction in set builder notation. c.
What is the domain of the function? d.
What is the range of the function? e.
Is this graph discrete or continuous?

M3 L11
1.
Given function 𝑓 on the Cartesian plane f(x) ={(x, 𝑥 2 + 1)│ − 𝟐 ≤ 𝒙 ≤ 𝟑 } a.
What is the domain of the function? b.
What is the range of the function? c.
Plot the function on the graph provided. d.
Is this a discrete graph or a continuous graph?
Set builder notation: for f(x) = 𝑥 2 + 1 graphed in the interval −2 ≤ 𝑥 ≤ 3 where x is a real number:
{(𝑥, 𝑥 2 + 1) | 𝑥 real, −2 ≤ 𝑥 ≤ 3}.
NOTE if a set is not specified we will assume the domain is real numbers.
In general, if 𝑓: 𝐷 → 𝑌 is a function with domain 𝐷 , then its graph is the set of all ordered pairs,
{(𝑥, 𝑓(𝑥)) | 𝑥 ∈ 𝐷}, thought of as a geometric figure in the Cartesian coordinate plane. (The symbol ∈ simply means “in.” The statement 𝑥 ∈ 𝐷 is read,
“ 𝑥 in 𝐷 .”)

M3 L11
Graph of 𝑓 : Given a function 𝑓 whose domain 𝐷 and the range are subsets of the real numbers, the graph of 𝑓 is the set of ordered pairs in the Cartesian plane given by
{(𝑥, 𝑓(𝑥)) | 𝑥 ∈ 𝐷}.
For Problem numbers 1 to 6: a) Write the ordered pairs generated by the following set builder notation sets. In each case state the (b) domain and the(c) range.
1.
{(x, 2x +1)│0 ≤ x ≤ 10 and x is an integer}
2.
{(x, 𝟏𝟎 ∙ 𝟑 𝒙 )│ 0 ≤ x ≤ 4 and x is an integer}
Problems number 3 to 6:
(a) Find the ordered pairs generated by the following sets; (b) Plot the ordered pairs. State the (c) domain and (d) range (e) state whether the graph is discrete or continuous.
3.
f = {(x, (𝒙 + 𝟏)(𝒙 − 𝟏) − 𝒙 𝟐
)│ -3 ≤ x ≤ 3 and x is an integer}
4.
f = {(x, 𝟑 −𝒙
)│ -3 ≤ x ≤ 3 and x is an integer}
5.
f = {(x, 𝒙 𝟑 )│ -3 ≤ x ≤ 3 and x is an integer}
6.
f = {(x, (𝒙 − 𝟐)(𝒙 − 𝟒)) │ 0 ≤ x ≤ 5 and x is real}
7.
Sketch the graph of the functions defined by the following formulas, and write the graph of 𝑓 as a set using set-builder notation.
(Hint: Assume the domain is all real numbers unless specified in the problem.) Show all work on your graph paper. Use one full side of graph per problem. a.
𝑓(𝑥) = 3𝑥 − 2 b.
𝑓(𝑥) = −3𝑥 − 2
} c.
𝑓(𝑥) = −
1
3 𝑥 + 2 , −3 ≤ 𝑥 ≤ 3 d.
𝑓(𝑥) = (𝑥 + 1) 2 − 𝑥 2 , −2 ≤ 𝑥 ≤ 5

M3 L11 e.
𝑓(𝑥) = (𝑥 + 1) 2 − (𝑥 − 1) 2
, −2 ≤ 𝑥 ≤ 4
8.
The figure shows the graph of 𝑓(𝑥) = −5𝑥 + 𝑐 . a.
Find the value of 𝑐 . b.
If the graph of 𝑓 intersects the 𝑥 -axis at 𝐵 , find the coordinates of 𝐵 .
9.
The figure shows the graph of 𝑓(𝑥) =
1
2 𝑥 + 𝑐 . a.
Find the value of 𝑐 . b.
If the graph of 𝑓 intersects the 𝑦 -axis at 𝐵 , find the coordinates of 𝐵 . c.
Find the area of triangle ∆𝐴𝑂𝐵 .