Transformations Exponential and Logarithm functions KUS objectives BAT

Transformations Exponential and Logarithm functions • KUS objectives BAT Understand sketch transformations of exponential and natural logarithm graphs Starter: xx

Graphs of Logarithimic Functions Open the Geogebra file ‘transformations of exp’ Explore moving the sliders to transform the graph of y = e x Extension: Explore transformations of y = lnx

BAT Understand sketch transformations of exponential and natural logarithm graphs WB 11 a y = 2 ex Sketch the graph of: y = 2 ex (0, 2) (For the same set of inputs (x), the outputs (y) double) (0, 1) y = ex

BAT Understand sketch transformations of exponential and natural logarithm graphs y = ex + 2 (0, 3) (For the same set of inputs (x), the outputs (y) increase by 2) (0, 1) y = ex

BAT Understand sketch transformations of exponential and natural logarithm graphs y = ex (For the same set of inputs (x), the outputs (y) ‘swap signs’ (0, 1) (0, -1) y = -ex

BAT Understand sketch transformations of exponential and natural logarithm graphs y = e 2 x (The same set of outputs (y) for half the inputs (x)) (0, 1) y = ex

BAT Understand sketch transformations of exponential and natural logarithm graphs y = ex + 1 y = ex (0, e) (0, 1) (The same set of outputs (y) for inputs (x) one less than before…) We can work out the y-intercept by substituting in x = 0 This gives us e 1 = e

BAT Understand sketch transformations of exponential and natural logarithm graphs y = ex y = e-x (0, 1) (The same set of outputs (y) for inputs with the opposite sign… (0, 1)

BAT Understand sketch transformations of exponential and natural logarithm graphs y = ln x + 2 (1, 2) (For the same set of inputs (x), the outputs (y) increase by 2) y = ln x (1, 0)

BAT Understand sketch transformations of exponential and natural logarithm graphs y = ln x Stretch factor 2 in x direction y = ln x/2 (1, 0) (2, 0)

BAT Understand sketch transformations of exponential and natural logarithm graphs y = 10 e-x WB 12 a Sketch the graph of: y = 10 e-x y = ex (0, 10) (0, 1) The graph of e-x, but with y values 10 times bigger… y = ex

BAT Understand sketch transformations of exponential and natural logarithm graphs y = ex WB 12 b Sketch the graph of: y = 3 + 4 e 0. 5 x y=3+ y = 4 e 0. 5 x (0, 7) (0, 4) (0, 1) The graph of e 0. 5 x, but with y values 4 times bigger with 3 added on at the end… y = e 0. 5 x

BAT Understand sketch transformations of exponential and natural logarithm graphs WB 13 a Sketch the graph of: y = 3 + ln(2 x)

BAT Understand sketch transformations of exponential and natural logarithm graphs WB 13 b Sketch the graph of: y = ln(3 - x)

BAT Understand sketch transformations of exponential and natural logarithm graphs

Practice Sketch these graphs: showing asymptotes and intersections Check your answers on geogebra

Chili Pepper Challenge - MEDIUM – now try a slightly trickier one HOT !!!– now a really tough one! Now swap questions

KUS objectives BAT Understand sketch transformations of exponential and natural logarithm graphs self-assess One thing learned is – One thing to improve is –

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