# 1 Gr-12-Maths Functions-Questions-Answers - Gr 12 Maths...

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Gr 12 Maths – Functions:QuestionsCopyright©The Answer21.The graph offis . . .1.1 If the inverse offis the reflection offin the line y =then the graph of the inverse is:A.B.C.D.(2)1.2 Consider the graph offgiven above.1.2.1Write down the equation of the given function and ofthe inverse function in the formy = . . .(2)1.2.2 Hence complete:(a)f(x) = . . .(b)f-1(x) = . . .1.2.3Show how the equation off-1could have beencalculated from the equation off.(2)1.2.4 Explain whyfandf-1are both one-to-onerelations.(2)Sketch the graphs offandf-1on the same set of axes,indicating also the liney =x.3.3Write down the equation off-1in the formf-1(x) =. . . .3.4Arefandf-1both functions?Why (not)?4.Given:g(x) = 3x- 2.Determine each of the following:4.1g-1(x)4.2xg1( )4.3g1x(6)5.1Sketch the graphy = 2x,indicating the coordinates ofany three points on the graph.(3)5.2Use the three points on the sketch to write down thecoordinates of three points on the inverse function ofy = 2x.(3)5.3On the same system of axes, sketch the inverse functionofy = 2xand the liney =x.5.4Describe the transformation from the graphy = 2xto itsinverse in words and give the rule for this transformation.(2)5.5Write down the equation of the inverse function in theformx= . . .[In Topic 4, you will convert this equation toy = . . . ](2)5.6Are both the above graphs functions? Why (not)?(2)5.7Write down the domain and the range of the graphs of:(a)y = 2x(b)x= 2y(4)6.Consider the functionfwheref(x) = 26.1Write down the domain and range off.6.2Sketch the graph offandgon the same set of axeswheregis the reflection offin the line y =x,(2)2.Consider the functionf(x) = -3x+ 6.2.1Write down the domain and range off.(2)2.2Determine the equation of the inverse offin the formf-1(x) = . . .(2)2.3Sketch the graphs of the functionsf,f-1andy =the same set of axes. What do you notice?(3)xon2.4Iff(1) = 3, thenf-1(3) = . . . ?2.5f(2) = 0(;)lies onfand(;)lies on3.1Write down the coordinates of thex- and y-intercepts of thefunctionf(x) = 2x+ 6and off-1, the inverse function off(1)f-1. (2). (4)3.2Sketch the graphs offandf-1on the same set of axes,indicating also the liney =x.3.3Write down the equation off-1in the formf-1(x) =. . . .3.4Arefandf-1both functions?Why (not)?4.Given:g(x) = 3x- 2.Determine each of the following:4.1g-1(x)4.2xg1( )4.3g1x(6)5.1Sketch the graphy = 2x,indicating the coordinates ofany three points on the graph.(3)5.2Use the three points on the sketch to write down thecoordinates of three points on the inverse function ofy = 2x.(3)5.3On the same system of axes, sketch the inverse functionofy = 2xand the liney =x.5.4Describe the transformation from the graphy = 2xto itsinverse in words and give the rule for this transformation.(2)5.5Write down the equation of the inverse function in theformx= . . .[In Topic 4, you will convert this equation toy = . . . ](2)5.6Are both the above graphs functions? Why (not)?(2)5.7Write down the domain and the range of the graphs of:(a)y = 2x(b)x= 2y(4)6.Consider the functionfwheref(x) = 26.1Write down the domain and range off.6.2Sketch the graph offandgon the same set of axeswheregis the reflection offin the line y =(4)(2)(2)(3)x2(2)x.

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Term
Spring
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Maro
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4 1 G, 4 3 g, 1 1 1 g, 4 2 1 g