Chapter 4 transformations Flashcards
What are the 4 things to remember when sketching a graph?
- Basic shape of graph positive or negative.
- y -intercept
- roots
- vertex
What does it mean on sketching if there is a repeated root?
What does it mean if there is a triple root?
Means it does not cross the x axis
It means it is a point of inflexion thing x^3 graph.
What two quadrants is a positive 1/x graph in?
Top right and bottom left.
What two quadrants is a negative 1/x graph in?
top left and bottom right.
What two quadrants is a positive 1/x^2 graph in?
top right and top left quadrant,
What two quadrants is the negative 1/x^2 graph in
bottom right and bottom left.
What happens when the numerator of the reciprocal increases?
When the numerator increases the graph pulls away from the axis.
What is unique about the reciprocal graph?
It has asymptotes which the graph approaches but never touches
What does it mean if it is a transformation of f(x+2) and f(x-2)
f(x+2) translation 2 to left.
f(x-2) translation 2 to right
What does it mean if it is a transformation f(x)+2 and f(x)+2
f(x)+2 2 up
f(x)-2 down
How would you change the equation of (x-1)^2
with the transformation of f(x)+2
would be (x-1)^2+2
How would you change the equation of (x-1)^2 with the transformation f(x-2).
you sub in x-2 for x.
(x-2-1)^2
What does the x^2 coefficient do?
The x^2 coefficient determines how steep the quadratic curve
How can you describe 2x^2 using function notation?
2f(x)
How can you describe (3x)^2 using function notation?
f(3x)
