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?
are original functions. 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?
are original functions. 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?
are original functions. 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?
are original functions. 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?
are original functions. 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?
are original functions. represent the respective transformed functions. Be sure only to highlight one original function at a time along with their transformed functions.