IM Alg1.4.10 Lesson: Domain and Range (Part 1)
Earlier, you saw a situation where the total number of times a dog has barked was a function of the time, in seconds, after its owner tied its leash to a post and left.
Less than 3 minutes after he left, the owner returned, untied the leash, and walked away with the dog. Could be an input of the function? Be prepared to explain your reasoning.
Could be an input of the function? Be prepared to explain your reasoning.
Could be an input of the function? Be prepared to explain your reasoning.
Could be an output of the function? Be prepared to explain your reasoning.
Could be an output of the function? Be prepared to explain your reasoning.
Could be an output of the function? Be prepared to explain your reasoning.
Decide whether each number is a possible input for the functions described here. Sort the cards into two groups—possible inputs and impossible inputs. Record your sorting decisions.
The area of a square, in square centimeters, is a function of its side length, , in centimeters. The equation defines this function.
A tennis camp charges $40 per student for a full-day camp. The camp runs only if at least 5 students sign up, and it limits the enrollment to 16 campers a day. The amount of revenue, in dollars, that the tennis camp collects is a function of the number of students that enroll. The equation defines this function.
The relationship between temperature in Celsius and the temperature in Kelvin can be represented by a function . The equation defines this function, where is the temperature in Celsius and is the temperature in Kelvin.
In an earlier activity, you saw a function representing the area of a square (function A) and another representing the revenue of a tennis camp (function R). Refer to the descriptions of those functions to answer these questions.
Here is a graph that represents function , defined by , where is the side length of the square in centimeters.
Name three possible input-output pairs of this function.
Earlier we describe the set of all possible input values of as “any number greater than or equal to 0.” How would you describe the set of all possible output values of ?
Function is defined by , where is the number of campers. Is 20 a possible output value in this situation? Explain your reasoning.
Is 100 a possible output value in this situation? Explain your reasoning.
Here are two graphs that relate number of students and camp revenue in dollars.
Which graph could represent function ?
Explain why the other one could not represent the function.
Describe the set of all possible output values of .
If the camp wishes to collect at least $500 from the participants, how many students can they have? Explain how this information is shown on the graph.
Explain how this information is shown on the graph.
Find f(x) for each x-value Clare listed. Describe what Clare’s trouble might be.
Use graphing technology to graph function d.
What do you notice about the graph?
Use a calculator to compute the value you and Clare had trouble computing.
What do you notice about the computation?
How would you describe the domain of function ?
Why do you think the graph of function looks the way it does?
Why are there two parts that split at , with one curving down as it approaches from the left and the other curving up as it approaches from the right?
Evaluate function at different -values that approach 2 but are not exactly 2, such as 1.8, 1.9, 1.95, 1.999, 2.2, 2.1, 2.05, 2.001, and so on. What do you notice about the values of as the -values get closer and closer to 2?