Chapter 4 Notes
Lesson 4-1
Problem 1: Analyzing a Graph
The graph shows the volume of air in a balloon as you blow it up, until it pops. What are the variables?
Describe how they are related at various points on the graph.
Got it? 1
What are the variables in the graph? Describe how the variables are related at various points on the graph.
Problem 2: matching a Table and a Graph
A band allowed fans to download its new video from its Web site. The table shows the total number of
downloads after 1, 2, 3, and 4 days. Which graph could represent the data shown in the table?
Got it? 2
Which graph could represent the data shown in the table?
Problem 3: Sketching a Graph
A model rocket rises quickly and then slows to a stop as its fuel burns out. It begins to fall quickly until the
parachute opens, after which it falls slowly back to Earth. What sketch of a graph could represent the height
of the rocket during its flight? Label each section.
Got it? 3
Suppose you start to swing yourself on a playground swing. You move back and forth and swing higher in the
air. Then you slowly swing to a stop. What sketch of a graph could represent how your height from the
ground might change over time? Label each section.
Lesson 4-2
Problem 1: Representing a Geometric Relationship
In the diagram, what is the relationship between the number of rectangles and the perimeter of the figure
they form? Represent this relationship using a table, word, an equation and a graph.
Got it? 1
In the diagram below, what is the relationship between the number of triangles and the perimeter of the
figure they form? Represent this relationship using a table, words, an equation and graph.
Problem 2: Representing a Linear Function
The table shows the relationship between the number of photos x you take and the amount of memory y in
megabytes (MB) left on your camera’s memory chip. Is the relationship a linear function? Describe the
relationship using words, an equation, and a graph.
Got it? 2
Is the relationship in the table a linear function? Describe the relationship using words, an equation, and a
graph.
Lesson 4-3
Problem 1: Classifying Functions as Linear or Nonlinear
A. The area A in square inches, of a pizza is a function of its radius r, in inches. Graph the function shown by
the table. Is the function linear or nonlinear?
B. The cost C, in dollars, of the sauce for a pizza is a function of the weight w, in ounces, or sauce used. Graph
the function shown by the table. Is the function linear or nonlinear?
Got it? 1
The table shows the fraction A of the original area of a piece of paper that remains after the paper has been
cut in half n times. Graph the function represented by the table. Is the function linear, or nonlinear?
Problem 2: Representing patterns and Nonlinear Functions
The table shows the number of blocks in each figure below as a function of the number of blocks on one edge.
What is the pattern you can use to complete the table?
Got it? 2
The table shows the number of new branches in each figure of the pattern below. What is the pattern you can
use to complete the table? Represent the function using words, an equation, and a graph.
Problem 3 Writing a Rule to Describe a Nonlinear Function
The ordered pairs (1, 2), (2, 4), (3, 8), (4, 16), and (5, 32) represent a function. What is a rule that represents
this function?
Got it? 3
What is a rule for the function represented by the ordered pairs (1, 1), (2, 4), (3, 9) (4, 16), and (5, 25)?
Lesson 4-4
Problem 1: Graphing a Function Rule
What is the graph of the function rule y = -2x + 1?
Got it? 1
What is the graph of the function rule y = ½ x – 1?
Problem 2: Graphing a Real-World Function Rule
The function rule W = 146c + 30,000 represents the total weight W, in pounds, of a concrete mixer truck that
carries c cubic feet of concrete. If the capacity of the truck is about 200 ft3, what is a reasonable graph of the
function rule?
Got it? 2
The function rule W = 8g + 700 represents the total weight W, in pounds, of a spa that contains g gallons of
water. What is a reasonable graph of the function rule, given that the capacity of the sap is 250 gallons?
Problem 3: Identifying continuous and Discrete Graphs
A local cheese maker is making cheddar cheese to sell at a farmer’s market. The amount of milk used to make
the cheese and the price at which he sells the cheese are shown. Write a function for each situation. Graph
each function. Is the graph continuous or discrete?
Got it? 3
Multiple Choice: The amount of water w is a wading pool, in gallons, depends on the amount of time t, in
minutes, the wading pool has been filling, as related by the function rule w = 3t. Graph the function rule. Is
the graph continuous or discrete?
Problem 4: Graphing Nonlinear Function Rules
A. Graph the function rule y = |x| - 4?
B. Graph the function rule y = x2 + 1
Got it? 4
What is the graph of the function rule y = x3 + 1?