Download Warm Up - Northwest ISD Moodle

What is a Function?
Height of
Candle
Describe what is
happening in this
function.
Time in Hours
What do these points stand for in
this scenario?
A:
Height of
Candle
A
B:
B
Time in Hours

Tom started the day with $50. He made $10
per hour at his job. Write an equation that
represents how much money (m) he had at
the end of the day working (h) hours.






What is the range if the domain is D:( -1, 1,
3, 6,) for these equations.
1.) y = 3x – 4
2.) y = -x - 6
3.) y = 5x – 5
4.) y = -2x – 12
5.) y = 3x + 4
John charges a flat fee of $50 plus $20 each hour for his services.
John typically doesn’t work more than 7 hours on 1 job.
50 +
20(0)
m
50
Money
h
Hours
What is my range for the function g(x) = 3x – 4
when my domain is d:( -1, 0, 2, 4)
Which letter or letters represent a relation.
A.)
C.) (-3,4) (-1,5) (1,6) (1,8)
B.)
-1
0
1
2
D.) f(x) = 3𝑥 2 - 4
-1
A
fish starts 40ft ahead of the
shark and swims at a rate of 15ft
per second.
Y
=
A
fish starts 40ft ahead of the
shark and swims at a rate of 15ft
per second.
Y
= 40 + 15x
A
fish starts 40ft ahead of the
shark and swims at a rate of 15ft
per second.
Y
= 40 + 15x
Y intercept
A
fish starts 40ft ahead of the
shark and swims at a rate of 15ft
per second.
Y
= 40 + 15x
A
fish starts 40ft ahead of the
shark and swims at a rate of 15ft
per second.
Y
= 40 + 15x
Slope
A
fish starts 40ft ahead of the
shark and swims at a rate of 15ft
per second.
Seconds
Distance(ft)
0
1
40
55
3
5
85
115

Slope Formula
= 15
Seconds
Distance(ft)
𝑦2 − 𝑦1
𝑥2 − 𝑥1
0
1
40
55
=
85 −55
3 −1
=
3
5
85
115
30
2

A fish starts 40ft ahead of the shark and swims at a
rate of 15ft per second.
(3,85)
(0,40)










A shark starts 50 ft behind a man swimming
frantically to shore. The Great white is towing a
piece of the dock at a pace of 40ft every second.
1.) Write the equation
2.) State the slope and y - intercept
3.) State the independent and dependent variable
4.) Make a table for the first 6 seconds
5.) Write the domain and range for that table
6.) Make a graph of the situation
7.) How many seconds has the shark swam if it has
travelled 910 ft?
8.) How far will the shark travel if he swims for an
entire minute?
9.) Does this situation represent direct variation?






Tina is on a weight losing kick and here are some
of her numbers based off pounds per month.
( 3, 145) ( 5, 135)
1.) What does the point ( 5, 135) mean in this
situation?
2.) What is the slope? What does this mean for this
situation.
3.) What is y – intercept? And what does this point
mean for this situation
4.) What is the independent and dependent
variable.

After month 3 John was 200 pounds. He was
losing 5 pounds per month.

Point ( 3, 200)

Slope = 5

Point ( 3, 200) Slope= 5
 Formula
y
– 𝑦1 = m(x – 𝑥1 )
y

Point ( 3, 200)
Slope = 5
– 𝑦1 = m(x – 𝑥1 )
(


-3, -3) m = 3
 y + 3 = 3(x + 3)
 Y + 3 = 3x + 9
-3=
-3
y = 3x + 6
 1.)
 2.)
 3.)
 4.)
 5.)
( 3, 5) m = 6
(-2, 6) m = -2
( 0, 5) m = 4
(-4, -6) m = ½
(-3 , 5) m=6





Chaz runs a Taxi service in New York that charges
a fee of .25c every mile. After 300 miles the
charge to use the taxi service equaled $77.50.
1.) What coordinate point did the story give us?
2.) What is the slope? What does this mean for this
situation.
3.) Write an equation for this situation.
4.) What is the independent and dependent
variable.

Zip Drain’s pool service makes a living draining the
water from pools. After 4 hours of work, 1500 gallons
of was left in Customer A’s pool. They have a 50 gallon
per hour quota.

1.) What coordinate point did the story give us?

2.) What is the slope? What does this mean for this
situation.

3.) Write an equation for this situation. (use point
slope first.


4.) What are the independent and dependent
variables?
5.) What is the x intercept and what does it mean?






Joseph’s painting service collected $545 after
painting 12 walls in the house. The charge $40 per
wall to paint.
1.) What coordinate point did the story give us?
2.) What is the slope? What does this mean for
this situation.
3.) Write an equation for this situation. (use point
slope first.
4.) What are the independent and dependent
variables?
5.) What is the domain and range for the first 6
walls






Joseph’s painting service collected $600 after
painting 12 walls in the house. The charge $40 per
wall to paint.
1.) What coordinate point did the story give us?
2.) What is the slope? What does this mean for
this situation.
3.) Write an equation for this situation. (use point
slope first.
4.) What are the independent and dependent
variables?
5.) What is the domain and range for the first 6
walls
 (-1,5)
-
y- =
(-4,8)
=
(x - )
y – 𝑦1 = m(x – 𝑥1 )
y – 𝑦1 = m(x – 𝑥1 )









y = 6x – 7
Y = -3x + 2
Y = -2x
Y = 2x
Y = 1/2x – 1
Y = 2x – 1
Y = -4x -12
Y = 2x + 8
Y = 3x + 10



Graph the following lines on the graph paper
provided for you.
Y = 2x + 6
Y = 2x + 2



Lines that have the same slope and different
y intercepts are Parallel lines.
Y = 1/2x – 4
Y = 1/2x + 5



Graph the following lines on the graph paper
provided for you.
Y = 2/3x - 6
Y = - 3/2x - 1

Lines that have slopes that are reciprocals
and different signs of each other. The
product of their slopes is -1.
Y
= 2/3x
Y = -3/2x
 Are
these sets of points
Parallel, Perpendicular or
Neither? Graph or Use slope
formula
 (0,-2)
(3,-1)
 (0, 3) (3,-5)

(0,-2) (3,-1)
 -1- (-2) =
3-0
1
3
(0, 3) (3,-5)
-5- 3
=
3-0
−8
3

My Brother is Perpendicular and Sister is
Parallel. If I am 5 what are my siblings?
Hint: I am slope

Brother:

Sister:


My Brother is Perpendicular and Sister is
Parallel. If I am 5 what are my siblings?

1
Brother: −
5

Sister: 5

Graph the equation below on your white
board.
Y
= 2x +1

What happens if we have these symbols.
Y
< 2x +1
Y > 2x + 1
Y ≥ 2𝑥 + 1
Y ≤ 2𝑥 + 1
y>
y≥
y<
y≤
y>
y<

y ≥ 2𝑥 + 1
 Strong
 Weak
 Positive
 Negative
shoesize
Age
A women’s
looks
Age
French
fries
Age of
toad




The stronger a correlation is, the closer it is
to 1
Ex: really strong : .9 or .8
Really weak
Ex: .1 or .2 or .3

Does a strong correlation mean that there is
a cause and effect relationship?
Write
Equation
for the
line
shown
A lion that is 50 ft away and runs at a
speed of 31ft per second chases a man
that runs at a speed of 22 ft per second.
A lion that is 50 ft away and runs at a
speed of 31ft per second chases a man
that runs at a speed of 22 ft per second.
Y = 31x – 50
Y = 22x
A lion that is 50 ft away and runs at a
speed of 31ft per second chases a man
that runs at a speed of 22 ft per second.
Y = 31x – 50
Y = 22x
Will the lion catch the man? If
so how long will it take and
how far will they run?
Y = 31x – 50
Y = 22x
2 ways to solve this
1.) Graph
2.) Use Algebra
Y = 31x – 50
Y = 22x
Use Algebra
31x – 50 = 22x
-22x
-22x
9x-50 = 0
+ 50 = +50
9x = 50
50
x =
𝑎𝑏𝑜𝑢𝑡 5.5
9
X = 4.5
Plug back in to either
equation
Y = 31(5.5) – 50
Y = 22(5.5)
Y = 121
Y = 121
Solution
(5.5, 121 )
1.) y = 2x – 1
y = -3x + 8
6.) y = -3x + 4
y = -2x + 4
2.) y = -1/2x + 10
y = 4x – 3
7.) y = 4x - 25
y = -2x + 25
3.) y = 2x – 7
y = 2x
8.) y = -35x + 200
y = 25x - 100
4.) y = -2/3x – 6
y=x+6
5.) y = x+ 4
y = 2x
The lion is jumping at a speed of 15 ft.
per sec to a man that is 18 ft. away and
is moving at 1 ft. per second. How long
will it take for the lion to get to the man.
1.) What is the
2.) What is the
3.) What is the
equations?
4.) What is the
equations?
equation for the lion?
equation for the man?
m and the b for both
solution to this system of
Josh started with $150 in his bank
account and gets paid $25 per week for
his chores. His sister Jade didn’t start
with any money but makes $35 per
week.
1.) Equation for Josh’s money
2.) Equation for Jade’s money
3.) What is the m and b for both
4.) What is the solution to this system of
equations?


The sum of two numbers is 25.
The larger number is 1 more than twice the
smaller number. What are the two numbers?


The sum of two numbers is 25.
The larger number is 1 more than twice the
smaller number. What are the two numbers?
X
– smaller number
 Y – larger number



The sum of two numbers is 25.
The larger number is 1 more than twice the
smaller number. What are the two numbers?
x + y = 25


The sum of two numbers is 25.
The larger number is 1 more than twice the
smaller number. What are the two numbers?
Y
= 1 + 2x


The sum of two numbers is 25.
The larger number is 1 more than twice the
smaller number. What are the two numbers?
Y
= 1 + 2x
X + y = 25





George bought 3 oranges and 2 apples and
paid $5.50.
Mireya bought 6 oranges and 1 apple and
paid $9.50.
1.) State the variables
2.) Write both equations
3.) Solve for the cost of an orange if you can
2*X
2X
x+x
2x
X*X
X
2
Example: 𝑥 * 𝑥 = 𝑥
2
5
7
2 5
Example: (𝑥 ) = 𝑥 10
Example:
5
𝑥
2
𝑥
=x
3
 What
is it?
 What is required?
 Any Rules?
 Whats my Reward?
 What
 Each
is it?
week, you will be given
roughly 15-25 questions that we
think will most likely show up on
your STAAR test.
What is required?
You have 1 week to answer these question.
Your target score is 80% or above.
What are the rules?
1.) Questions are not to be completed
during the school day/ except Invest.
2.) Must show work.
3.) No cheating.
4.) Must be turned in on time.
Reward?
Fort Worth Zoo
Perot Museum
Main Event Bowling
Skate Town









Which are true
A.) as x increases, y
decreases without bound.
B.) Range: y>1
C. as x increases y
decreases with bound.
D. Range = all real #’s
E. Domain: x > 1
F. Domain: all real #’s
1

Bob’s bank account started with $800 and
grew at a rate of 8% per year. Which equation
models this behavior.
x




a.) y = 800(.08)
x
B.) y = 800(1.08)
x
C.) y = 800(.8)
D.) y = 800(1.8) x






Which equation matches the table the best.
2
A.) 2x + 4
B.) 2x + 4
x
C.) 4(1.4)
x
D.) 3(1.5)
Hint - Statplot
x
y
0
4
1
6
2
9
3
11
4
15

Determine which table is linear, exponential,
or neither
x
y
x
y
0
2
x
y
1
3
0
2
0
2
2
4.5
1
3.5
1
3
3
6.75
2
5
2
5
3
6.5
3
8
 (3x



+ 2y) + (2x – 3y)
3x + 2x = 5x
2y – 3y = -y
5x - y
 (3x
+ 2y) – ( 2x – 3y)

Distribute the negative
 (3x + 2y) + ( -2x + 3y)
 3x – 2x = x
 2y + 3y = 5y

x + 5y
Pg
691
Pg 692
Pg 693
Pg 706
:
:
:
:
3,4,6
9 – 12
17
3 - 10





Simplify ( x – 7 )
2
A.) 𝑥 2 + 49
B.) 𝑥 2 - 14x + 49
C.) 𝑥 2 − 49
D.) 2x - 14
 Pg.
723-724 : 1,4,5,9,11
 Pg. 733: 1,2,3,7,9
 Pg. 745 : 13,16



4
21𝑥 𝑦
3𝑥 𝑦
.)
1
3
2
2
A.) 7x y
2
2
2
B.) 18 x y
C.) 7x y
2
3
2 3
D.) 18 x y
X
+ 2 𝑥 + 6𝑥 + 12
2
X
+ 2 𝑥 + 6𝑥 + 16
2
(𝑥
+
2
7)
A.) 𝑥 2 + 49
2
 B.) 𝑥 + 14𝑥 + 49
2
 C.) 2𝑥 + 14
2
 D.) 𝑥 − 49




2
F(x) = 3(x + 5) + 4
A.) What is the Vertex? ( _, _)
B.) What is the axis of symmetry? X = _
Which of the following could be
the vertex of the parabola
𝑦 = 𝑥 2 + 2𝑥 − 24?
a.) (-6, 0)
b.) (0,-24)
c.) ( 4,0)
d.) (-1,-25)
2
What is the function f(x) = 2(x – 3) + 2
written in Standard from.
2
 A.) 2𝑥 − 6𝑥 + 20
2
 B.) 2𝑥 − 12𝑥 + 20
2
 C.) 2𝑥 − 12𝑥 + 11
2
 D.) 2𝑥 − 6𝑥 + 11


What is the value of d for the equation
3
 (𝑥
7




− 2)(𝑥 + 𝑑)
A.) 4
B.) .4
C.) -4
D.)
7
3

What are the roots for
𝑥
2
+ 3𝑥 − 7
3
1(-7)
3
(1)





Simplify 16
A.) 4
B.) -4
C.) both A & B
D.) None of the above

Breaking down Radicals-

1.) List all the perfect square roots.


4 9 16 25 36 49 64 81 100
= 2,3,4,5,6,7,8,9,10



For Example
27
9* 3
3 3