Interpreting Functions
Linear, Quadratic, and Exponential Models
Modeling
Reasoning/Reasoning with Equations and Inequalities
Seeing Struture in Expressions/Creating Equations
100
The function f is defined by f(x)=7/3x-7
Find and use the slope of f(x) to plot the next point, starting at (0,-7).
Next point = (3,0).
100
Jada slides down a slide at a rate of
f(s)=-3s+9
where f represents Jada's height, in feet, off the ground s seconds after going down the slide. How many feet off the ground is Jada after 2 seconds?
Jada is 3 feet off the ground after 2 seconds.
100
Jordan tracks the attendance for 5 Raven's home games.
G1=65,000
G2=66,500
G3=68,200
G4=69,800
G5=71,500
Does the attendance model linear or exponential growth? Justify. (Hint: Think about what a linear function vs an exponential function looks like when graphed)
Linear growth. The difference between each game is not large enough to show exponential growth (exponential growth has a sharp curve).
100
Let f(x) = 2x + 100, where x can be any real number. Axel says that all of the outputs of this function are greater than 100. Do you agree? Why or why not? What is Axel's reasoning?
No. The function is greater than 100 for non-negative numbers, which is why Axel said this.
However, Axel may have forgotten that functions can have negative number inputs.
For example, f(-1) = 2(-1) + 100 = 98 which is less than 100.
So if x is a negative number, the output will be less than 100.
100
Charlie models two basketball game halves:
1st half = 3x^2+2x-5 and
2nd half = x^2-4x+7
Add the polynomials for the full game expression.
4x^2-2x+2
200
A.APR.A.1
A sequence is defined by an = -4(n + 3)+12, where n is a positive integer.
What is a6?
a6 = -24.
200
F.LE.B.5-1
TyQuan is saving up money to buy a laptop. The function f(x)=$20x+$50 represents the total amount of money f in dollars, in the TyQuan's bank account, x weeks after he started saving for that laptop. What does the number 20 represent in the function f?
The slope; TyQuan is earning $20 per week which is the increase in dollars in the student's bank account each week.
200
Kishai tries to model her weekly braiding revenue as function R
R(x) = 50x, where x = number of clients.
The table below represents her actual revenue...
2 clients = $95
5 clients = $240
8 clients = $370
12 clients = $520
Compare Kishai's model to the actual data. Is it a good fit? Justify.
Debate! :)
Predicted:
R(2)=100
R(5)=250
R(8)=400
R(12)=600
Actual:
2 clients = $95
5 clients = $240
8 clients = $370
12 clients = $520
(If they can accurately justify their reasoning they get the points)
200
Terrance claims that 2x^2-8=0 has no real solutions because 'you can't take the square root of a
negative.' Is he correct?
While he is correct that you cannot take the square of a negative number, that doesn't apply to here.
When moving -8 to the other side of the equal sign to solve, it becomes positive.
x = -2, 2
200
I'm tired of making questions.
Free points
300
F.IF.A.1
The function f is defined by
f(x)=-3(x+1)^2+19
for all real numbers x. What is the range of f?
Less than or equal to 19 OR (-∞, 19)
300
A cell phone company charges $60.00 a month for up to 1 gigabyte of data. The cost of additional data is 5 cents per megabyte.
Write a linear equation that can be used to determine the user's monthly bill where d represents the number of additional megabytes used and c represents the total charges at the end of the month.
c = $60+0.05d
300
A.1.M.7 - A.CED.A.3
Mr. Homan is ordering this year’s supply of pencils and pens for the classroom. Each pencil costs $0.10, each pen costs $0.75, and Mr. Homan will spend a total of $235 on pencils and pens.
Which additional piece of information is sufficient to determine the number of pencils and the number of pens that he will order? (Pick one)
a) The number of pencils purchased last year will be equal to the number of pens purchased this year.
b) The number of pens purchased this year will be three times the number of pencils purchased this year.
c) The total cost of the pens purchased this year will be greater than the total cost of the pencils purchased this year.
d) The total cost of the pencils and pens purchased last year will be three times the total cost of the pencils and pens purchased this year.
b) The number of pens purchased this year will be three times the number of pencils purchased this year. (y = 3x)
300
Zion got a Playstation for his birthday. He wants to purchase a Playstation Plus plan, but doesn’t know which one to choose. Plan A is $9.99 a month. Plan B is $24.99 every three months. Plan C is $79.99 annually.
a) About how much do plans B and C cost per month?
b) How much cheaper is plan C compared to plan A per month?
c) Which plan should Zion get to save the most money each year?
a) B = $8.33 per month, C = $6.66 per month
b) Plan C is $3.33 cheaper per month
c) Zion should get plan C
300
Patricia and Sakia are starting a snack business. They are selling fruity and chocolate pebble crispy treats.
They charge $2 for the fruity pebble treats and $3 for the chocolate pebble treats. In their first week, they make $33. That same week, they end up selling 14 treats total.
Create a system of equations to represent their bake sales. Use x to represent the number of fruity pebble treats and y to represent the number of chocolate pebble treats.
$33 = $2x + $3y
14 = x + y
400
F.BF.B.3
The function f(x)=x^2 models a basic basketball shot arc. Describe the transformation for each:
a) g(x)=(x-3)^2+5
b) h(x)=-2x^2
c) k(x)=(x+1)^2-4
a) g(x): RIGHT 3, UP 5 (vertex at (3,5))
b) h(x): REFLECTED over x-axis, STRETCHED by 2 (narrower, opens down)
c) k(x): LEFT 1, DOWN 4 (vertex at (-1,-4))
400
F.LE.B.5
An object is dropped off the roof of a building. The function h(x)=-32x^2+128 models the height, h(x) , in feet, of the object above the ground x seconds after it is dropped. What is the best interpretation of h(2) = 0 in this context?
The object is no longer falling and has hit the ground at 2 seconds.
Explanation: h(x) represents the height of the object in feet. x represents time in seconds. So when x = 2 (2 seconds have passed), h(x) = 0 (the object's height is 0).
400
Emoni is selling cookies at a concert. Her profit can be modeled by function P...
P(x)=-2x^2+40x-150
where x is the price per cookie. Find the price per cookie that maximizes profit and what her maximum profit would be.
Vertex: (10, 50); $10 per cookie, $50 max profit.
400
A.REI.C.6
A system of equations is given
{(y,=,9x,-,1),(y,=,2x,+,3):}
What is the value of 𝑥 in the solution (𝑥,𝑦) to the system?
Enter your answer as a fraction.
x=4/7
400
A.SSE.B.3.b
Function f is defined as f(x)=-x^2+4x-9 What is the minimum value of f(x)? (Hint: The minimum value of f(x) is the y-coordinate coordinate of the vertex, which is also your k value). Show your work.
y = -5
500
F.IF.B.5
At a movie theater, a popcorn maker is filled with 2,000 popcorn kernels. The kernels pop at a rate of 40 kernels per minute. Create a function P(m) that represents the number of kernels that haven't been popped after m minutes, and then determine the domain of that function.
P(m) = (2,000/40) - m
Domain: 0 ≤ m ≤ 50
500
F.LE.A.2
Kyran is training to run a 10 km race. During week 0 of training, each practice run is 3 km. Each week after, Kyran increases the length of his practice run by 25%.
a) Write a function representing the length of Kyran's practice runs in week n.
b) Create a table showing the length of practice runs for weeks 1-7 using the function you created.
Part a: f(n) = 3*(1.25)^n
Part b: f(0) = 3
f(1) = 3.75
f(2) = 4.69
f(3) = 5.86
f(4) = 7.32
f(5) = 9.16
f(6) = 11.44
f(7) = 14.3
500
When is Mr. Homan's birthday?
500
A1.R.4
Deontae claims that if an equation has no exponents greater than 1, then the equation must be linear.
Which equation can be used to show that Deontae's claim is false?
a) y=x
b) y=|x|
c) x+y=1
d) y-x^2=1
b) y=|x|
500
A.SSE.A.2
Which of the following expressions can be written as (𝑎𝑥 +𝑏)(𝑎𝑥−𝑏) , where 𝑎 and 𝑏 are integers? Select all that apply.
a) x^2-9
b) x^2-11
c) 4x^2-1
d) 4x^2-2
e) 9x^2-4
a)x^2-9
c)4x^2-1
e)9x^2-4
Every answer where the coefficient and constant are BOTH perfect squares (i.e. 1, 4, 9...) and they are being substracted.