D AY 16: D OMAIN AND R ANGE .
I NTRODUCTION Sometimes it is important to know the kind of inputs and also the outputs of a function that we are working with. Like in computer programs, when a value outside the allowed set of values in input into a program, the computer considers it invalid. All these can be explained and determined under the concept of domain and range. We are going to learn how to identify and determine appropriate domain and range of functions.
V OCABULARY
Take a measuring instrument for height, in inches. Get a sample of 5 students. Take a pen and a paper for recording purposes.
1. First list the name of the five students. 2. Measure their height and record it against them.
3. Order the students based on their height so that 1 the tallest student and 5 the shortest among the five. The lists should be ordered from 1 to 5. 1 is the tallest and 5 the shortest.
4. Now make another list with three columns separated by Arrows as shown below. Label the arrows are shown in the diagram below. Shows arrows of an input with the corresponding output. 1 List here LIST 2 HERE Their 3 THE Listing Height 4 Heights NAMES Function Allocating Function 5 Function diagram in 4 to be filled and input and corresponding output identified by arrows
5. What is the domain of a function? Set of all inputs of a function
6. Identify the domains of the listing and the height allocating functions. Listing function, the domain is the set {1,2,3,4,5} Height allocation function, the domain is the set {𝑏, 𝑐, 𝑑, 𝑒, 𝑓} Where 𝑏, 𝑐, 𝑑, 𝑒 and 𝑓 are names of the five students
7. What is a range of a function? Set of all outputs of a function Listing function, the range is the set {𝑏, 𝑐, 𝑑, 𝑒, 𝑓} Where 𝑏, 𝑐, 𝑑, 𝑒 and 𝑓 are names of the five students
8. Identify the range of the listing and the height allocating functions. Height allocation function, the range is the set {𝑏, 𝑐, 𝑑, 𝑒, 𝑓} Where 𝑏, 𝑐, 𝑑, 𝑒 and 𝑓 height of the students
Example Find the domain of the function 𝑧 = 𝑦 + 7. Solution The square root of a negative number is not defined in the set of real numbers. Therefore, 𝑦 + 7 ≥ 0 hence 𝑦 ≥ −7 The domain is −7, ∞) because y is not defined for values of 𝑦 < −7 . The range is 0, ∞) because for all values of 𝑦 ≥ −7, the values of y will be greater than zero.
Domain and range from a graph The domain is the set of all x -coordinates in the function of the graph and the range is the set of all y -coordinates in the function of the graph.
Example Find the domain and range of the graph below.
Solution The domain is the set of all x -coordinates where the graph exists. Therefore, the domain is the set of all real values of x such that −4 ≤ 𝑦 ≤ 4. The domain is −4,4 The range is the set of all y -coordinates where the graph exists. Therefore, the range is the set of all real values of y such that 0 ≤ 𝑧 ≤ 4. The range is 0,4
H OMEWORK Find the domain and range of the graph below.
THE END
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