D AY 16: D OMAIN AND R ANGE . I NTRODUCTION Sometimes it is - - PowerPoint PPT Presentation

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D AY 16: D OMAIN AND R ANGE . I NTRODUCTION Sometimes it is - - PowerPoint PPT Presentation

Jun 23, 2023 586 likes •907 views

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

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DAY 16: DOMAIN AND RANGE.

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INTRODUCTION

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.

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VOCABULARY

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Take a measuring instrument for height, in inches. Get a sample of 5

  • students. Take a pen and a paper

for recording purposes.

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  • 1. First list the name of the five

students.

  • 2. Measure their height and record it

against them.

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  • 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.

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  • 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.

Function diagram in 4 to be filled and input and corresponding output identified by arrows

Listing Function

1 2 3 4 5 LIST HERE THE NAMES

Height Allocating Function

List here Their Heights

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  • 5. What is the domain of a function?

Set of all inputs of a function

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  • 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

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  • 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

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  • 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

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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.

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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.

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Example Find the domain and range of the graph below.

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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

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HOMEWORK

Find the domain and range of the graph below.

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THE END