Chapter 4 - Graphs and Transformations Flashcards
If p is a root of the function y= f(x), where does the graph cross the x-axis?
It crosses at the point:
(p,0).
Where does the graph
Y= k
—
x
Have asymptotes?
Asymptotes at x= 0 and at y= 0.
The lines are in top right and bottom left section of the graph.
Where does the graph
Y= -k
—
x
Have asymptotes?
Asymptotes at x= 0 and at y= 0.
The lines are in the top left and bottom right section of the graph.
Where does the graph
Y= k
——
x^2
Have asymptotes?
Asymptotes at x= 0 and at y= 0.
The lines are in the top right and top left sections of the graph.
Where does the graph
Y= -k
——
x^2
Have asymptotes?
Asymptotes at x= 0 and at y= 0.
The lines are in the bottom right and bottom left sections of the graph.
How do you find the x-coordinates at the point of intersections of two curves y= f(x) and
y= g(x).
You find the solutions of the equation:
f(x) = g(x).
what happens to the graph of y= f(x) when it is translated by y= f(x) + a?
It is translated by the vector:
(0)
(a)
It moves vertically.
what happens to the graph of y= f(x) when it is translated by y= f(x + a)?
It is translated by the vector:
(-a)
(0 )
It moves horizontally.
When you translate a function, what happens to the asymptotes?
They get translated too by the same amount.
what happens to the graph of y= f(x) when it is stretched by y= af(x)?
It is stretched by a scale factor of a in the vertical direction.
what happens to the graph of y= f(x) when it is stretched by y= f(ax)?
It is stretched by a scale factor of:
1
—
a
In the horizontal direction.
what happens to the graph of y= f(x) when it is reflected by y= -f(x)?
It is reflected in the x-axis.
what happens to the graph of y= f(x) when it is reflected by y= f(-x)?
It is reflected in the y-axis.
What kind of shape does a repeated root in y= f(x) cause?
E.g. (x + 1)^2
It causes a parabola shape
down-stationary-up
Or
(Up-stationary-down)
What kind of point does a triple repeated root in
Y= f(x) cause?
E.g. (x + 1)^3
It causes a point of inflection.
Down-stationary-down
Or
(Up-stationary-up)
