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-3 -2 -1 1. -8642 -2 3 * 6 4 2 0 2 46 8 10 2 2- -8-6 -4 -2 8 4 2 -2 4 -6 5 Determine whether these statements about -8 -10 the functions in question 4 are true or false. a i The point (-3, 2) lies on the graph of 4 Find the domain and range of each of these this function. i The image of x=-2 is y= 3. li When x=-4, y 0. bi The graph of this function crosses the functions. x-axis at (-2, 0). il The point (0, -1) does not lie on the graph of this function. li There is only one value of x for which y=-2.

-3 -2 -1 1. -8642 -2 3 * 6 4 2 0 2 46 8 10 2 2- -8-6 -4 -2 8 4 2 -2 4 -6 5 Determine whether these statements about -8 -10 the functions in question 4 are true or false. a i The point (-3, 2) lies on the graph of 4 Find the domain and range of each of these this function. i The image of x=-2 is y= 3. li When x=-4, y 0. bi The graph of this function crosses the functions. x-axis at (-2, 0). il The point (0, -1) does not lie on the graph of this function. li There is only one value of x for which y=-2.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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MODELLING CONSTANT RATES OF CHANGE: LINEAR FUNCTIONS 5.1 ci When x= 9, y = 0. ii As the values of x increase, the corresponding values of y decrease. iii The vertical line x=-7 intersects this graph once. di The line y = 0 cuts the graph of this function twice. A V(variation from 37 C) 4.5 b 4 -2- 2 3.5 3 -3 -2 8 -6 -4 -2 -1 -1 2.5 -2 ii There are two values of x for which 2 y= 2. ii As the values of x increase, so do the corresponding values of y. 1.5 0.5 0.5 ei The line y= 0.5 intersects the graph of this function twice. -2 -1 2 3 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 18 2 ii The line y = 1.5 intersects the graph of this function twice. Times in hours since application started to work -2 i The value x= 2 has no image. a State whether or not the relation represented in the graph is a function, giving the reason for your answer. b State the domain and the range. 2 4 6 8 10 6 Find the domain of each of these functions if it is known that the range is 1-3, -2, -1, 0, 1, 2). -8 -6 -4 -2 Explain their meaning in the context of the problem. c Write down the missing coordinate for cach ordered pair from the graph: 2 a x 2x +1 > 2 -8 -6 4 -2 0 2 4 6 8 b x c y= -x+ 2 (0.2.), (0.8,). 2), (2, ). d State the temperature of the person at the start of the application. e After how many hours was the temperature of this person equal to 37°C? f During what period of time did the temperature of the person increase? Over what period did it decrease? 8. 7 A special application measures the temperature of a person and records on a graph its variation from 37°C, considered to be the average optimum temperature. The application stops working when the temperature of the person is optimum. B64 6 4 2 2 4 -2 -4 -6 5 Determine whether these statements about the functions in question 4 are true or false. -8 For a function f, the notation y=f(x) means that x (an element of the domain, the input) is mapped through the function / to y (an element of the range, the output). -10 a i The point (-3, 2) lies on the graph of this function. 4 Find the domain and range of each of these functions. ii The image of x =-2 is y = 3. iii When x=-4, y= 0. bi The graph of this function crosses the x-axis at (-2, 0). ii The point (0, -1) does not lie on the graph of this function. Note that: • fix) is read "f of x". • If y = f(x) then x is said to be the independent variable and y is the dependent variable. • Different variables and names can be used for functions, such as d = v(t), m C(n), etc. HINT Be careful! fx) does not mean "f times x. -2 0. -2 iii There is only one value of x for which y=-2. -6.4 216 217 Number and algebra Functions
Transcribed Image Text:MODELLING CONSTANT RATES OF CHANGE: LINEAR FUNCTIONS 5.1 ci When x= 9, y = 0. ii As the values of x increase, the corresponding values of y decrease. iii The vertical line x=-7 intersects this graph once. di The line y = 0 cuts the graph of this function twice. A V(variation from 37 C) 4.5 b 4 -2- 2 3.5 3 -3 -2 8 -6 -4 -2 -1 -1 2.5 -2 ii There are two values of x for which 2 y= 2. ii As the values of x increase, so do the corresponding values of y. 1.5 0.5 0.5 ei The line y= 0.5 intersects the graph of this function twice. -2 -1 2 3 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 18 2 ii The line y = 1.5 intersects the graph of this function twice. Times in hours since application started to work -2 i The value x= 2 has no image. a State whether or not the relation represented in the graph is a function, giving the reason for your answer. b State the domain and the range. 2 4 6 8 10 6 Find the domain of each of these functions if it is known that the range is 1-3, -2, -1, 0, 1, 2). -8 -6 -4 -2 Explain their meaning in the context of the problem. c Write down the missing coordinate for cach ordered pair from the graph: 2 a x 2x +1 > 2 -8 -6 4 -2 0 2 4 6 8 b x c y= -x+ 2 (0.2.), (0.8,). 2), (2, ). d State the temperature of the person at the start of the application. e After how many hours was the temperature of this person equal to 37°C? f During what period of time did the temperature of the person increase? Over what period did it decrease? 8. 7 A special application measures the temperature of a person and records on a graph its variation from 37°C, considered to be the average optimum temperature. The application stops working when the temperature of the person is optimum. B64 6 4 2 2 4 -2 -4 -6 5 Determine whether these statements about the functions in question 4 are true or false. -8 For a function f, the notation y=f(x) means that x (an element of the domain, the input) is mapped through the function / to y (an element of the range, the output). -10 a i The point (-3, 2) lies on the graph of this function. 4 Find the domain and range of each of these functions. ii The image of x =-2 is y = 3. iii When x=-4, y= 0. bi The graph of this function crosses the x-axis at (-2, 0). ii The point (0, -1) does not lie on the graph of this function. Note that: • fix) is read "f of x". • If y = f(x) then x is said to be the independent variable and y is the dependent variable. • Different variables and names can be used for functions, such as d = v(t), m C(n), etc. HINT Be careful! fx) does not mean "f times x. -2 0. -2 iii There is only one value of x for which y=-2. -6.4 216 217 Number and algebra Functions
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