Sketch the graph and state the domain and range. g ( x ) = x + 2 x − 1

We have, g ( x ) = x + 2 x − 1 We observe that for x = 1 , g x is not defined. Now, we will sketch the graph of g x by taking different values of x . x 0 - 1 2 g x - 2 - 1 2 4 We obtain the graph of the given function as shown below. Let f : A → B , then, the set A is known as the domain of f and the set B is known as the co-domain of f . The set of all f - images of elements of A is known as the range of f or image of set of A under f and is denoted by f A . Thus, f = f x : x ∈ A = Range of f . Here, by looking at the graph we can say that Domain is x ∈ R , x ≠ 1 and Range is y ∈ R , y ≠ 1 .

Sketch the graph and state the domain and range. f : x → − log ⁡ ( x − 1 )

We have, f : x → − log ⁡ ( x − 1 ) Now, we will sketch the graph of f x by taking different values of x . Clearly, we observe that for x = 1 , f x is not defined. x 2 3 4 f x = − log ⁡ ( x − 1 ) 0 ∵ log 1 = 0 - log 2 = - 0 . 30102999 - log 3 = - 0 . 4771212547 We obtain the graph of the given function as shown below. Let f : A → B , then the set A is known as the domain of f and the set B is known as the co-domain of f . The set of all f - images of elements of A is known as the range of f or image of set of A under f and is denoted by f A . Thus, f = f x : x ∈ A = Range of f . Here, by looking at the graph we can say that Domain is x ∈ 1 , ∞ and Range is y ∈ R - 1 .

Sketch the graph and state the domain and range. g : x → 3 cos ⁡ x + 2

We have, g : x → 3 cos ⁡ x + 2 Now, we will sketch the graph of g x by taking different values of x . x 0 - 1 2 g x 5 3 . 62091 0.7516 We obtain the graph of the given function as shown below. Let f : A → B , then the set A is known as the domain of f and the set B is known as the co-domain of f . The set of all f - images of elements of A is known as the range of f or image of set of A under f and is denoted by f A . Thus, f = f x : x ∈ A = Range of f . Here, by looking at the graph we can say that Domain is x ∈ R and Range is y ∈ - 1 , 5 .

Draw the graph of a possible function for the domain x ∈ R and range y ∈ R .

Let f : A → B . Then, the set A is known as the domain of f and the set B is known as the co-domain of f . The set of all f - images of elements of A is known as the range of f or image of set of A under f and is denoted by f A . Thus, f = f x : x ∈ A = Range of f . Here, Domain is x ∈ R and Range is y ∈ R . Consider an example, where f x = x , where domain and range is R Now, we make the table for y = x by taking different values of x . x - 1 0 1 2 f x - 1 0 1 2 Drawing the graph for f x .

Draw the graph of a possible function for the domain ] - ∞ , ∞ [ and Range [ 3 , ∞ [

Let f : A → B . Then, the set A is known as the domain of f and the set B is known as the co-domain of f . The set of all f - images of elements of A is known as the range of f or image of set of A under f and is denoted by f A . Thus, f = f x : x ∈ A = Range of f . Here, Domain is ] − ∞ , ∞ [ and Range is [ 3 , ∞ [ . Consider an example, y - 3 = x 2 + 2 x + 1 . Here domain is ] − ∞ , ∞ [ and range is [ 3 , ∞ [ Making the table for y = x 2 + 2 x + 4 x 0 1 - 1 - 2 y 4 7 3 4 Now, drawing the graph.

Draw the graph of a possible function for the domain 0 ≤ x < 6 and Range is − 3 ≤ y < 2 .

Let f : A → B . Then, the set A is known as the domain of f and the set B is known as the co-domain of f . The set of all f - images of elements of A is known as the range of f or image of set of A under f and is denoted by f A . Thus, f = f x : x ∈ A = Range of f . Here, domain is 0 ≤ x < 6 and Range is − 3 ≤ y < 2 . Consider an example where f x = x 6 - x , here domain is 0 ≤ x < 6 and range is − 3 ≤ y < 2 . Making the table by taking different values of x . x 0 1 2 f x 0 2 . 23606 2 . 828427 Drawing the graph for f x .

Consider the graph of the piecewise function y = f x , where − 3 ≤ x ≤ 6 . Find the equations for the function, including an interval of the domain that applies to each part.

We have, y = f x , where − 3 ≤ x ≤ 6 . By looking at the graph we can make the following equations which are as below: For, − 3 ≤ x ≤ − 1 , f x = - x For, − 1 < x ≤ 2 , f x = 2 x + 3 and for, 2 < x ≤ 6 , f x = 7 which can be summarised as below: f ( x ) = − x , − 3 ≤ x ≤ − 1 2 x + 3 , − 1 < x ≤ 2 7 , 2 < x ≤ 6 Note: It is also possible to include - 1 in the second interval rather than the first and 2 in the third interval rather than the second.

E M B I B E

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 2 - Representing Relationships: Introducing Functions>Exercise 2D

Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Representing Relationships: Introducing Functions, Exercise 20: Exercise 2D

Author:Natasha Awada, Paul La Rondie, Laurie Buchanan & Jill Stevens

Natasha Awada Mathematics Solutions for Exercise - Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Representing Relationships: Introducing Functions, Exercise 20: Exercise 2D

Attempt the practice questions on Chapter 2: Representing Relationships: Introducing Functions, Exercise 20: Exercise 2D with hints and solutions to strengthen your understanding. Mathematics : Analysis and Approaches Standard Level Course Companion solutions are prepared by Experienced Embibe Experts.

Questions from Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Representing Relationships: Introducing Functions, Exercise 20: Exercise 2D with Hints & Solutions

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IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 2 - Representing Relationships: Introducing Functions>Exercise 2D>Q 2

Sketch the graph and state the domain and range.

g (x) = \frac{x + 2}{x - 1}

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IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 2 - Representing Relationships: Introducing Functions>Exercise 2D>Q 2

Sketch the graph and state the domain and range.

$f : x \to - \log (x - 1)$

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IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 2 - Representing Relationships: Introducing Functions>Exercise 2D>Q 2

Sketch the graph and state the domain and range.

$g : x \to 3 \cos x + 2$

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IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 2 - Representing Relationships: Introducing Functions>Exercise 2D>Q 3

Draw the graph of a possible function for the domain $x \in R$ and range $y \in R$ .

MEDIUM

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IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 2 - Representing Relationships: Introducing Functions>Exercise 2D>Q 3

Draw the graph of a possible function for the domain $] - \infty, \infty [$ and Range $[3, \infty [$

MEDIUM

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IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 2 - Representing Relationships: Introducing Functions>Exercise 2D>Q 3

Draw the graph of a possible function for the domain $0 \leq x < 6$ and Range is $- 3 \leq y < 2$ .

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IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 2 - Representing Relationships: Introducing Functions>Exercise 2D>Q 3

Draw the graph of a possible function for the domain $x > 0$ and range $y > 0$ .

EASY

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 2 - Representing Relationships: Introducing Functions>Exercise 2D>Q 5

Consider the graph of the piecewise function $y = f (x)$ , where $- 3 \leq x \leq 6$ . Find the equations for the function, including an interval of the domain that applies to each part.

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