1. 6.2
Describing Functions
What are some characteristics that you can use to describe functions?

2. Since b = 0, the graph is proportional.
EXAMPLE 1
Since b = 0, the graph is proportional.
Vance charges $20 an hour to plow the snow off of driveways. The equation y = 20x gives the cost y in dollars for x hours. State whether the relationship between the time and the cost is proportional or nonproportional. Then graph the function.
Insert a blank graph in place of this one

3. EXAMPLE 2
A rectangular field is x feet wide and x + 2 feet long. The equation y = x2 + 2x gives the area of the field in square feet. Determine whether the relationship between x and y is linear and, if so, whether it is proportional.
The graph is not a line, so the relationship is not linear. Since it is not a line, it is also not proportional.

4. EXAMPLE 3
State whether the relationship between x and y in y = 2x – 3 is proportional or nonproportional. Then graph the function.
Insert a blank graph in place of this one
nonproportional

5. State whether the relationship between x and y in
EXAMPLE 4
State whether the relationship between x and y in
y = x2 – 1 is linear and, if so, if it is proportional or nonproportional. X -1 1 2 3 Y
not linear, nonproportional

6. EXAMPLE 5
Lenora is making rice at a women’s shelter. The table shows y, the total number of cups of water she needs to use for x cups of rice.
Use the data to draw a graph. Is the relationship between x and y linear? Explain.
Use your graph to predict the number of cups of water to use when using 10 cups of rice.
Yes, it is linear; the graph of the solutions lie in a straight line.
25 cups of water

7. What are some characteristics that you can use to describe functions?
Answer:
A function can be linear or nonlinear. A linear function can be proportional or nonproportional.

8. Texas Essential Knowledge and Skills
The student is expected to:
Proportionality—8.5.H
Identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems.
Proportionality—8.5.G
Identify functions using sets of ordered pairs, tables, mappings, and graphs.
Mathematical Processes
8.1.D
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.