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DATE : September, 33
ESSENTIAL QUESTION: How are the domain and range of an
equation different than the domain and range of a function?
AGENDA:
1. Warm up
2. Guided practice
3. Independent practice
Homework: Finish this worksheet and turn in on Friday 9/29
Mastery Test I on solving multi-step equations RETAKE on 9/28
Thursday early release day!
1) Clear your desk except for paper/pencil
2) Copy the DATE and TOPIC
In ordered pairs:
1. {(3, 2), (-1, 4), (0, 3), (-3, 5), (-2, -2)}
2. {(3, 6), (5, 7), (7, 7) (8, 9)}
Domain: Range:
Domain and Range
{3, -1, 0, -2, -3} {2, 4, 3, 5, -2}
Is the relation a function? Why or why not?
Is the relation a function? Why or why not?
Domain: Domain:
Range: Range:
3. 4.
{6, 2, 1, 0}
{3, 4, 5}
Is the relation a function? Why or why not?
5. 6.
{3, -4, 7, 1}
{-5, 3, -2}
Domain: Domain:
Range: Range:
Is the relation a function? Why or why not?
7. 8.
{-2, 1, 2, 3}Domain: Domain:
Range: Range:{-2, 0, 1, 2, 4}
Is the relation a function? Why or why not?
In equations or functions:
1. With fractions, the domain is limited by the
denominator which cannot equal 0.
2.
5 + x ≠ 0
xy
5
7Domain:
Range: All R
All real numbers (R) except -5
x ≠ -5
In 𝑓 𝑥 =12
𝑥 −3, where x ≠ 3
Why must the domain be specified?
If it is not specified it will not be a function
Domain: Range:
In word problems: The situation determines the
domain and the range. Find reasonable domain
and range for each of the functions.
1. The function f(x) = 175 + x represents the
amount of money in a savings account that
started with $175 after a deposit of x dollars.
What are a reasonable domain and range of
the function?
Whole numbers
where x > 0
Whole numbers
where f(x) > 175
Domain: Range:
2. Elaine is in the business of repairing home
computers. She charges a base fee of $50 for
each visit and $25 per hour for her labor. The
total cost c(x) for a home visit and x hours of
labor is modeled by the function rule:
c(x) = 50 + 25x.
All whole numbers,
where x > 0All multiples of 25,
where x > 50
Domain: Range:
3. The function f(x) = 10 – x represents the
amount of change you receive after paying for
an item that costs x dollars with a $10 bill
0 < x < 10 0 < x < 10
Domain: Range:
4. The function f(x) = 20 – x represents the
amount of change you receive after paying for
an item that costs x dollars with a $20 bill.
Domain: Domain:
Range: Range:
all real numbers
y < 2
1. 2.
Is the relation a function? Why or why not?
In graphs: The graph determines the domain and range.
1. Choose 3 values for x. Substitute into equation to find its output.
Graph ordered pairs, draw line and fill in the missing information.
x-intercept:
y-intercept:
Rate of change:
Increasing or decreasing:
End behaviors:
(2, 0)
(0, -4)
2
increasing
As x approaches -∞, y approaches -∞;
As x approaches ∞, y approaches ∞
y = 2x – 4
y = 2(-1) – 4
y = 2(0) – 4
y = 2(2) – 4
(-1,-6)
(0, -4)
(2, 0)
Graphing functions
x y
-1 -6
0 -4
2 0
2. y = -2
3𝑥 + 2
x-intercept:
y-intercept:
Rate of change:
Increasing or decreasing:
End behaviors:
(3, 0)
(0, 2)
-2/3
decreasing
As x approaches -∞, y approaches ∞;
As x approaches ∞, y approaches -∞
y = -2
3(3) + 2
y = -2
3(0) + 2
y = -2
3(−3) + 2
(3, 0)
(0, 2)
(-3, 4)
2.Elaine is in the business of repairing
home computers. She charges a
base fee of $50 for each visit and
$25 per hour for her labor. The total
cost c(x) for a home visit and x
hours of labor is modeled by the
function rule:
c(x) = 50 + 25x.
Domain: Range:
3.The function f(x) = 10 – x represents
the amount of change you receive
after paying for an item that costs x
dollars with a $10 bill
Domain: Range:
4. The function f(x) = 20 – x represents the
amount of change you receive after
paying for an item that costs x dollars
with a $20 bill.
Domain: Range: