# Constructing Graphs (Grades 11-12)

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## Constructing Graphs

1.

A model rocket is launched and its altitude tracked over time. At 1 second the rocket is at 210 ft, at 3 seconds it is at 450 ft, and at 6 seconds it is at 360 ft.

a) Sketch a graph of the rocket's altitude over time and label.

b) Is the graph linear?

c) What is the approximate height which the rocket reaches?

a) Sketch a graph of the rocket's altitude over time and label.

b) Is the graph linear?

c) What is the approximate height which the rocket reaches?

2.

Karen opens a savings account and deposits $50 each month into it. Sarah opens a savings account as well and deposits $1. Each month she will deposit twice as much as the previous month.

a) Sketch and label a graph showing the total savings in each girl's account. Make the graph show the first year that the girls have the accounts.

b) After 6 months who has saved more?

c) Did both girls choose saving plans that are practical? Explain your reasoning.

a) Sketch and label a graph showing the total savings in each girl's account. Make the graph show the first year that the girls have the accounts.

b) After 6 months who has saved more?

c) Did both girls choose saving plans that are practical? Explain your reasoning.

3.

The altitude of a weather balloon is tracked after it is released. The data at 1, 2, 6, and 30 minutes shows altitudes of 780, 1,600, 4,850, and 22,000 feet.

a) Graph and label this relationship.

b) Is this graph linear or non-linear? Explain your reasoning.

a) Graph and label this relationship.

b) Is this graph linear or non-linear? Explain your reasoning.

4.

Tony starts an ice cream stand and tracks his net profit over time. After 1 month his net income is -$400. After 2 months the net income is $400. At 3 months the net income is $1,100 and after 5 months it is $2,200.

a) Using the tables, fill in the given values and the find the pattern to fill in the remaining values for the first 10 months of business.

b) If this trend continues, what is the most that Tony can ever expect to make in a month?

c) How far was Tony in debt when he started the business?

a) Using the tables, fill in the given values and the find the pattern to fill in the remaining values for the first 10 months of business.

b) If this trend continues, what is the most that Tony can ever expect to make in a month?

c) How far was Tony in debt when he started the business?

5.

a) Use the table to fill in the given values and missing values to this sequence.

(2,-1), (3,1), (5,5)

b) Write a function to represent this relation.

c) Graph the relation.

(2,-1), (3,1), (5,5)

b) Write a function to represent this relation.

c) Graph the relation.

6.

a) Enter given and missing values from this set in the tables.

(_,18), (-3,_), (-2,_), (-1,3), (0,2), (_,3), (_,6), (3,_), (4,_), (5,27)

b) Construct the function that describes this set.

c) Is this a linear relationship?

(_,18), (-3,_), (-2,_), (-1,3), (0,2), (_,3), (_,6), (3,_), (4,_), (5,27)

b) Construct the function that describes this set.

c) Is this a linear relationship?

7.

a) Graph and label the function [math]f(x)=-2(x-2)^2+5.[/math]

b) Does this function have a maximum or minimum value?

c) What is the maximum/minimum y value?

d) At what x value does the maximum/minimum occur?

b) Does this function have a maximum or minimum value?

c) What is the maximum/minimum y value?

d) At what x value does the maximum/minimum occur?

8.

Keely sells skateboards at a kiosk. She has been selling them for $45 each and averaging 10 sales per day. She found that if she drops the price by $3 each, she sells 1 more skateboard each day.

a) Define the function that describes her total revenue, dependent upon the amount she adjusts her price and quantity of sales.

b) Graph and label this relationship.

c) Can Keely make more money than she is right now? If so how much can she make per day?

d) What is the price she should be selling the skateboards at in order to maximize profit?

a) Define the function that describes her total revenue, dependent upon the amount she adjusts her price and quantity of sales.

b) Graph and label this relationship.

c) Can Keely make more money than she is right now? If so how much can she make per day?

d) What is the price she should be selling the skateboards at in order to maximize profit?

9.

a) Graph the relationship for the absolute value of [math]3x-2.[/math]

b) Is there a maximum or minimum value on this graph? If so what is it?

b) Is there a maximum or minimum value on this graph? If so what is it?

10.

Cara is ordering stickers for craft supplies and she can get the stickers she needs from 2 different suppliers. Company A sells the stickers for $0.30 per sheet plus $5 shipping. Company B sells the stickers for $0.40 per sheet plus $2 shipping.

a) Construct functions to describe the cost of ordering from each store.

b) Graph and label the functions.

c) If Cara orders 20 sheets which company should she order from?

d) At what point is the cost the same?

a) Construct functions to describe the cost of ordering from each store.

b) Graph and label the functions.

c) If Cara orders 20 sheets which company should she order from?

d) At what point is the cost the same?

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