Students' Worksheet : Exponential Function Transformations

Exponential Function Transformation - Student Activity

[b][size=150]The exponential function is [color=#ff0000]y = a[/color][/size][/b][b][size=150][color=#ff0000][sup]x[/sup][/color] , denoted by function f. [br] [/size][/b][b][size=150][color=#ff0000][math]\cdot[/math][/color][/size][/b][br]The transformed basic function is [b][size=150][color=#ff0000]y = a[/color][/size][/b][size=150][color=#ff0000][sup]x+c[/sup][/color][color=#ff0000]+ b[/color]with changing the parameter using glider tools[/size][size=150].[/size][br][b][color=#ff0000][size=150][br]Note[/size][/color][/b]: The 'slider' feature on the x-y coordinate plane can be used to change the [color=#ff0000][b]a, b, and c[/b][/color] values [br] for the following exercises. To do so, place the cursor and hold it on the dot of the slider and [br] slide it to the desired m and b values.[br] To move the slider to a different location on the x-y plane, place the cursor and hold it on the line [br] of the slider and move it to the desired location.[br][br][b][color=#ff00ff]Note: You can zoom in or out with the mouse.[/color][/b]

Exponential Function Transformations #1

Activity #1

[b][size=150]Perform the following exponential function transformation:[br][/size][/b][br][b]We do the change of parameter "a". Assume a=2.[br][br][/b] The basic function is [b][color=#ff0000]y=a[/color][/b][b][size=150][color=#ff0000][sup]x[/sup][/color][/size][/b] , denoted by function f.[br][br] [color=#0000ff]Set a=2. [br] Change the parameter "a" using glider tools.[br][/color][br][b][color=#ff00ff] Observe the transformation of the exponential function.[br][/color][/b] (1) When a > 1, what the characteristic of the graph?[br] (2) When 0 < a < 1, what the characteristic of the graph?[br] (3) What difference between [b][color=#ff0000]a > 1[/color][/b] and [b][color=#ff0000]0 < a < 1[/color][/b] ? [br] (4) When a = 1, what the characteristic of the graph?[br] (5) When a = 0, what the characteristic of the graph?

Exponential Function Transformations #2

Activity #2

[b][size=150]Perform the following exponential function transformation:[br][/size][/b][br][b]Parameter "b" changing. [/b][b]Assume a=2.[/b] [br][br] The new function is [b][color=#ff0000]y= [/color][/b][b][color=#ff0000]a[/color][/b][b][size=150][color=#ff0000][sup]x[/sup][/color][/size][/b][b][color=#ff0000] + b[/color][/b] , denoted by function f.[br][br] [color=#0000ff]Set a=2. [br] Change the parameter "b" using glidder tools.[br][/color][br][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]exponential [/color][/b][b][color=#ff00ff]function.[br][/color][/b] (1) When b > 0, what the characteristic of the graph? Comparing with the origin [b][color=#ff0000]y= [/color][/b][b][color=#ff0000]a[/color][/b][b][size=150][color=#ff0000][sup]x[/sup][/color][/size][/b] [br] (2) When b < 0, what the characteristic of the graph? Comparing with the origin [b][color=#ff0000]y= [/color][/b][b][color=#ff0000]a[/color][/b][b][size=150][color=#ff0000][sup]x[br][/sup][/color][/size][/b] (3) When b = 0, what the characteristic of the graph? Comparing with the origin [b][color=#ff0000]y= [/color][/b][b][color=#ff0000]a[/color][/b][b][size=150][color=#ff0000][sup]x[/sup][/color][/size][/b]

Exponential Function Transformations #3

Activity #3

[b][size=150]Perform the following exponential function transformation:[br][/size][/b][br][b]Parameter "c" changing. [/b][b]Assume a=2.[/b] [br][br] The new function is [b][color=#ff0000]y= [/color][/b][b][color=#ff0000]a[/color][/b][b][size=150][color=#ff0000][sup]x+c[/sup][/color][/size][/b] , denoted by function f.[br][br] [color=#0000ff]Set a=2. [br] Change the parameter "c" using glidder tools.[br][/color][br][b][color=#ff00ff] Observe the transformation of the [/color][/b][b][color=#ff00ff]exponential [/color][/b][b][color=#ff00ff]function.[br][/color][/b] (1) When c > 0, what the characteristic of the graph? Comparing with the origin [b][color=#ff0000]y= [/color][/b][b][color=#ff0000]a[/color][/b][b][size=150][color=#ff0000][sup]x[/sup][/color][/size][/b] [br] (2) When c < 0, what the characteristic of the graph? Comparing with the origin [b][color=#ff0000]y= [/color][/b][b][color=#ff0000]a[/color][/b][b][size=150][color=#ff0000][sup]x[br][/sup][/color][/size][/b] (3) When c = 0, what the characteristic of the graph? Comparing with the origin [b][color=#ff0000]y= [/color][/b][b][color=#ff0000]a[/color][/b][b][size=150][color=#ff0000][sup]x[/sup][/color][/size][/b]

Formative Test#1

Question #1

[b][size=150]According to graph above, what the value of parameter "a", both a red and blue graph? Based on the [color=#ff0000]y = [b]a[/b][b][size=150][sup]x[/sup][/size][/b][/color][/size][/b]

Formative Test#2

Question #2

[b][size=150]According to graph above, what the value of parameter a and b? Based on the [color=#ff0000][b][color=#ff0000]y= [/color][/b][b][color=#ff0000]a[/color][/b][b][size=150][color=#ff0000][sup]x[/sup][/color][/size][/b][b][color=#ff0000] + b[/color][/b][b][size=150][sup][br][/sup][/size][/b][/color][/size][/b]

Formative Test#3

Question #3

[size=150]According to graph above, which one of the following function is true?[br][/size](a) [size=150]y= a[size=150][sup]x[/sup] [/size][/size][br](b) [size=150]y= a[size=150][sup]x[/sup][/size] + b[/size][br](c) [size=150]y= a[size=150][sup]x+c[br][/sup][/size][/size](d) [size=150]y= a[size=150][sup]x+c[/sup][/size] + b[br][br][/size]Based on your answer, determine the value of each parameter (a, b, or c)!