1. Chapter 2 Section 2 Domain and Range 2 If Q = f ( t ), then: (a) the domain of f is the set of input values, t, which yield an output value. (b) the.

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1

Chapter 2 Section 2 Domain and Range 2

If Q = f ( t ), then: (a) the domain of f is the set of input values, t, which yield an output value. (b) the range of f is the corresponding set of output values, Q. Page 69 Blue Box3

If there are no restrictions, domain of the function is the set of all real numbers. Page 694

If there are no restrictions, domain of the function is the set of all real numbers. However, if a function is used to model a real-world situation, the domain and range of the function are often restricted: Page 695

Is there any restriction in the domain regarding the house painting example: n = f(A) = A/250? Page 69 Example 16

If there any restriction in the domain regarding the house painting example: n = f(A) = A/250? A (area of house) > 0 Page 697

If there any restriction in the range regarding the house painting example: n = f(A) = A/250? Page 698

If there any restriction in the range regarding the house painting example: n = f(A) = A/250? n (# of gal. of paint) > 0 (book says n ≥ 0 (if gal. rounded to nearest whole #) Page 699

When a function is used to model a real situation, it may be necessary to modify the domain and range. Page 6910

Let's revisit our "cricket" function: Page 69 Example 211

Let's revisit our "cricket" function: Domain and/or range restrictions? Page 6912

Let's revisit our "cricket" function: Domain and/or range restrictions? In theory, none... Page 6913

Domain and/or range restrictions? Page14

Domain and/or range restrictions? if 0 ≤ R ≤ R max Page15

Domain and/or range restrictions? if 0 ≤ R ≤ R max, then 40 ≤ T ≤ T max Page16

Using a Graph to Find the Domain and Range of a Function Page 7017

To review: Domain = the set of input values on the horizontal axis which give rise to a point on the graph; Range = corresponding set of output values on the vertical axis. Page 7018

A sunflower plant is measured every day t, for t ≥ 0. The height, h ( t ) centimeters, of the plant can be modeled by using the logistic function: (a) Using a graphing calculator or computer, graph the height over 80 days. (b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Page 70 Example 319

(a) Using a graphing calculator or computer, graph the height over 80 days. Page 7020

(b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Page 7021

(b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Domain: t ≥ 0 Page 7022

(b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Domain: t ≥ 0 BUT... Page 7023

(b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Domain: t ≥ 0 Since sunflower will die... ? Page 7024

(b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Domain: t ≥ 0 Since sunflower will die 0 ≤ t ≤ T, where T is the day that the sunflower dies. Page 7025

(b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Range? Page 7126

A reminder of what the graph looks like. Page 7027

(b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Range? What is the minimum value of h? Page 7128

(b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Range? What is the minimum value of h? When t = 0, h = 10.4 cm. Page 7129

(b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Range? What is the minimum value of h? When t = 0, h = 10.4 cm. Maximum value of h? Page 7130

(b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Range? What is the minimum value of h? When t = 0, h = 10.4 cm. Maximum value of h? As t increases, h(t) approaches 260 cm. Page 7131

(b) What is the domain of this function? What is the range? What does this tell you about the height of the sunflower? Range? 10.4 ≤ h(t) ≤ 260 Page 7132

Using a Formula to Find the Domain and Range of a Function Page 7133

State the domain and range of g, where: g(x) = 1 / x Page 71 Example 434

State the domain and range of g, where: g(x) = 1 / x Domain: all real numbers, except that x ≠ 0 Page 7135

State the domain and range of g, where: g(x) = 1 / x Domain: all real numbers, except that x ≠ 0 Range = ? Page 7136

State the domain and range of g, where: g(x) = 1 / x Domain: all real numbers, except that x ≠ 0 Range = ? Range is all real numbers except 0 (since 1/x can't = 0 ). Page 7137

Page38

Find the domain of: Page 71 Example 539

Find the domain of: What can't x = ? Page 7140

Find the domain of: If we eliminate complex numbers, domain = ? Page 7141

Find the domain of: Domain: x > 4 Page 7142

Find the range of: Page 7143

Find the range of: Since domain: x > 4, range = ? Page 7144

Find the range of: Since domain: x > 4, range: f(x) > 0 Page 7145

End of Section