 # 7 ask is the exponential function increasing or

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7. Ask:Is the exponential function increasing or decreasing?(Increasing).Ask:Is the inverse function increasing or decreasing?(Increasing).8.Remind learners how to write the inverse of a function:f–1(x) and label the graph as above.9.Write the equation of the exponential function on the board:y= 2x10. Find the equation of the inverse function with learners:x= 2yUse logarithms to makeythe subject of the formula.y= log2x11. Tell learners to write this equation next to the log graph they drew.12. Ask learners to draw another Cartesian plane with the liney=xdrawn in, then ask them todraw the functiony=21x_i.Some learners may need to be reminded that because the base lies between 0 and 1, thefunction will decrease.Grade 12 Term 1 Maths lesson plans.indb1092018/12/171:09 PM
110Grade 12 MATHEMATICS Term 1TOPIC 2, LESSON 6: LOGARITHMIC FUNCTIONS13. Once learners have drawn the exponential function ask them to draw the inverse of thefunction. Remind them to consider the fact that it must be reflected in the liney=xand alsoto consider the intercepts and the asymptotes.14. Once learners have completed their sketches, draw them on the board for learners to checkand correct their work if necessary.15. As you are drawing the graphs, discuss the intercepts and the asymptotes. Ensure thatlearners can see the connections between the exponential function and its inverse.54321123456789-3-2-1-1-2-3yxf-1(x) = logx12f(x) =x1216. If learners didn’t write the equation of each function on the diagram, tell them to do so now.17. Use the diagram to discuss other aspects of functions and their inverses before doing a fullyworked example with learners.18. Ask each question and give learners a minute or so to answer before discussing andcorrecting it with themQuestionSolutionNotesWrite down the range off(x) =21x_iyϵ(0;)ory> 0Point out that once the range of thefunction has been determined, it shouldbe clear that the domain of the inversefunction will be made up of the same setof numbers.Write down the domain off–1(x) =logx21xϵ(0;)orx> 0Write down the values of xfor whichf(x) ≤ 4xϵ(–2;)orx> –2These values can be read directly fromthe graph or calculated algebraically.Write down the values of xfor whichf–1(x) > –2xϵ(0;4)or 0 <x< 4Grade 12 Term 1 Maths lesson plans.indb1102018/12/171:09 PM
111Grade 12 MATHEMATICS Term 1TOPIC 2, LESSON 6: LOGARITHMIC FUNCTIONS19. Tell learners that you are going to do one fully worked example from a past paper. Learnersshould write the example in their books and make notes as they do so.Example:Given:f(x) = logaxwherea> 0.S;131_iis a point on the graph off.yx0S=f1–;–13a) Prove thata= 3b) Write down the equation ofh, the inverse off, in the formy= ...c) Ifg(x) = –f(x), determine the equation ofg.

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Geometric progression
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