Chapter 6 Transformations And Functions And Their Graphs Flashcards
What is a shift?
It is a translation of a graph of a function without changing its shape or orientation in the x-y plane.
How can translations be expressed?
y=f(x-h) +k
What are reflections?
Transformations that flip a graph in the x-y plane without changing its shape
How would you apply reflection to a function to flip it up or down?
By taking the original function o(x) and putting a negative sign next to it
new(x) = -old(x)
How would you reflect a Functions graph left or right?
By taking the original function and adding a negative to the input value
new(x) = old(-x)
Reflect the following function up/down
D(t) = 150 - r(t)
y(t) = -D(t) + 150
Symmetry
The property of functions that remain unchanged under reflection
Even functions
Functions whose graphs are symmetric about the y-axis
Example p(x) = x^2
Odd functions
Functions whose graphs are symmetric about the origin of the x y axis.
Example p(x) = x^3
If f(-x) = f(x) for all values of x it is…
An even function
If f(-x) = -f(x) for all values of x then it is…
An odd function
What is vertical stretch?
Essentially think of a wave that is amplified but the intervals, that is the point in which the wave hits the x axis, do not change.
What does a negative stretch factor do?
It reflects the graph along the x axis and then amplifies it.
How do you stretch a function?
By multiplying the output of the function
What value does the stretch factor need to be to stretch the graph?
It must be greater than 1
What value must the stretch factor be in order for the function to be compressed?
It must be greater than 0 but less than 1
How is the average rate of change impacted by the stretch factor?
The average rate of change is also multiplied by the stretch factor
How would you do a horizontal stretch on a function?
By multiplying the functions input
What is the order of resolution for combined transformations?
y=Af(B(x-h)) + k
Horizontal stretch then shift
Vertical stretch then shift
If the stretch factor is less than 0 for a horizontal stretch, how would it be reflected?
It would be reflected about the y axis
