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Determining Constraints

Total questions: 15

Worksheet time: 26mins

Name
Class
Date
1.

Constraints are things that _______ options in problems.

a)

limit

b)

expand

2.

a)

all real numbers

b)

12n5212\le n\le52

c)

12n12512\le n\le125

d)

52n12552\le n\le125

3.

An object is in the air for a total of 8 seconds and reaches a maximum height of 24ft before landing on the ground. If h(t) represents the height of the object after t seconds, find the range

a)

0y80\le y\le8

b)

0y240\le y\le24

4.
What is the range of the graph?
a)
-2 < y < 10
b)
-3 < x < 3
c)
-2 ≤ y ≤ 10
d)
-3≤ x ≤ 3
5.

Emma is planning a birthday party and wants balloons and party hats. She has $20 to spend. Each balloon costs $1, and each party hat costs $2. She wants to buy at least 5 balloons. She needs to have enough items so that each of her 12 friends gets either a balloon or a hat. Emma doesn't want to buy more than 15 items in total.

Let x represent the number of balloons and y represent the number of party hats. Select all the inequalities represented by the situation.

a)

x \le 0

b)

x \ge 0

c)

y \ge 0

d)

y \le 0

6.

Which inequality represents "less than 4 ounces"?

a)

x > 4

b)

x < 4

c)

x \le 4

d)

x \ge 4

7.

Which inequality represents "at least 5 people attending"?

a)

x > 5

b)

x < 5

c)

x \le 5

d)

x \ge 5

8.
Janice is working as a babysitter for the Harold Family.  They plan to leave for their date at 7:00 pm  and be back by 12:00 am.  If the equation f(x) = 15x + 20 models the amount that Janice will earn, where x is the number of hours she works, and f(x) is the total money she earns, what is an appropriate domain?
a)
any value between 0 and 5
b)
any value between 15 and 20
c)
any value between -1 and 1
d)
any value greater than 0
9.

Janice is working as a babysitter for the Harold Family. They plan to leave for their date at 7:00 pm and be back by 12:00 am. If the equation f(x) = 15x + 20 models the amount that Janice will earn, where x is the number of hours she works, and f(x) is the total money she earns, what is an appropriate range?

a)

any value between 0 and 20

b)

any value between 20 and 125

c)

any value between 20 and 95

d)

any value greater than 0

10.

Greenlings are a group of fish that share common features. The function G(x)=10x2+100x+44G\left(x\right)=-10x^2+100x+44 models the number of greenlings caught, in thousands, in the United States, from 2006 to 2013.

Determine the constraints.

​ (a)   < x <​ (b)  

Choose from the below words
0
7
5
10.42218
3
11.

Greenlings are a group of fish that share common features. The function G(x)=10x2+100x+44G\left(x\right)=-10x^2+100x+44 models the number of greenlings caught, in thousands, in the United States, from 2006 to 2013.

Determine the constraints.

​ (a)   < y <​ (b)  

Choose from the below words
44
294
0
254
12.

A photographer was attempting to get the best angle of a building from a helicopter. The height of the helicopter over time is represented by the equation, H(x)=1(x40)2+1000H\left(x\right)=-1\left(x-40\right)^2+1000 , where 𝑥 is the time (in minutes) and 𝐻 is the height of the helicopter (in feet).

We want to know WHEN the height is the greatest. What key feature do we need?

a)

x-intercept

b)

y-intercept

c)

vertex

d)

domain

13.

A photographer was attempting to get the best angle of a building from a helicopter. The height of the helicopter over time is represented by the equation, H(x)=1(x40)2+1000H\left(x\right)=-1\left(x-40\right)^2+1000 , where 𝑥 is the time (in minutes) and 𝐻 is the height of the helicopter (in feet).

We want to know WHEN the height is the greatest. Is that going to be the x of the vertex or y?

a)

x-value of the vertex

b)

y-value of the vertex

14.

A photographer was attempting to get the best angle of a building from a helicopter. The height of the helicopter over time is represented by the equation, H(x)=1(x40)2+1000H\left(x\right)=-1\left(x-40\right)^2+1000 , where 𝑥 is the time (in minutes) and 𝐻 is the height of the helicopter (in feet).

At how many minutes is the height the greatest?

(a)  

15.

In 1965, a Ford Mustang cost $2,600. While most cars lose value, a 1965 Mustang in immaculate condition can be worth over $30,000. The function G(x)=20(x10)2+395G\left(x\right)=20\left(x-10\right)^2+395 models the price of the 1965 Mustang in the United States since 1965.

In what year is the price the lowest?

(a)