Investigation - Transformation of Functions

Vertical Transformations.

Investigate how adding a constant (k-use the slider) to an original function transforms the original function. What general rules can you conclude?[br][br] [math]f\left(x\right),g\left(x\right),h\left(x\right)[/math] are original functions. [math]Tf\left(x\right),Tg\left(x\right),Th\left(x\right)[/math] represent the respective transformed functions. Be sure only to highlight one original function at a time along with their transformed functions

Horizontal Translations

Investigate how adding a constant (k-use the slider) to the input transforms the original function. What general rules can you conclude?[br][br] [math]f\left(x\right),g\left(x\right),h\left(x\right)[/math] are original functions. [math]Tf\left(x\right),Tg\left(x\right),Th\left(x\right)[/math] represent the respective transformed functions. Be sure only to highlight one original function at a time along with their transformed functions

Y-axis Reflection

Investigate how placing a negative sign in front of the x input [f(x) - Tf(x) = f(-x)] transforms the original function. What general rules can you conclude?[br][br] [math]f\left(x\right),g\left(x\right),h\left(x\right)[/math] are original functions. [math]Tf\left(x\right),Tg\left(x\right),Th\left(x\right)[/math] represent the respective transformed functions. Be sure only to highlight one original function at a time along with their transformed functions. Please note that moving the slider k now translates the original function, but this should allow you to confirm the transformation of placing a negative sign in front of the x input [f(x) - Tf(x) = f(-x)]

X-axis Reflection

Investigate how placing a negative sign in front of the function [f(x) - Tf(x) = -f(x)] transforms the original function. What general rules can you conclude?[br][br] [math]f\left(x\right),g\left(x\right),h\left(x\right)[/math] are original functions. [math]Tf\left(x\right),Tg\left(x\right),Th\left(x\right)[/math] represent the respective transformed functions. Be sure only to highlight one original function at a time along with their transformed functions. Please note that moving the slider k now translates the original function, but this should allow you to confirm the transformation of placing a negative sign in front of the x input [f(x) - Tf(x) = -f(x)].

Vertical Stretching and Compressing

Investigate how multiplying by a constant (k-use the slider) transforms the original function [Tf(x) = kf(x)]. What general rules can you conclude?[br][br] [math]f\left(x\right),g\left(x\right),h\left(x\right)[/math] are original functions. [math]Tf\left(x\right),Tg\left(x\right),Th\left(x\right)[/math] represent the respective transformed functions. Be sure only to highlight one original function at a time along with their transformed functions.

Horizontal Stretching and Compressing

Investigate how multiplying the input x by a constant (k-use the slider) transforms the original function [Tf(x) = f(kx)]. What general rules can you conclude?[br][br] [math]f\left(x\right),g\left(x\right),h\left(x\right)[/math] are original functions. [math]Tf\left(x\right),Tg\left(x\right),Th\left(x\right)[/math] represent the respective transformed functions. Be sure only to highlight one original function at a time along with their transformed functions.