Transformations
Inverses
End Behavior
Roots
Asymptotes
100
f(x) + 2 Represents this type of transformation
Vertical shift 2 units up
100
What is the inverse of (2x+3)/4
What is 2x-(3/2)
100
The end behavior of the function y = x^2
As x -> ∞, f(x) -> ∞
As x -> -∞, f(x) -> ∞
100
The roots to f(X) = (x-2)(x+3)
What is 2, -3
100
the line that goes from left to right
What is a horizontal asymptote?
200
f(x - 4) Represents this type of transformation
Horizontal shift 4 units right
200
What is the inverse of 3x+1
What is (x-1)/3
200
The end behavior of f(x) = -x^3 + 2x^2 - 4x + 1
As x -> -∞ , f(x) -> ∞
As x -> ∞ , f(x) -> -∞
200
When a root happens more than once the exponent on the factor changes and this is called ____________
What is multiplicity
200
a line that goes down and up
What is a vertical asymptote?
300
f(x) - 5 Represents this type of transformation
Vertical Shift 5 units down
300
The inverse of g(x)=(8-5x)/4
What is -(4x-8)/5
-
300
The end behavior of the function f(x) = log (x + 2)
As x -> -2, f(x) -> -∞
As x -> ∞ , f(x) -> ∞
300
What has to happen for a graph to turn around on the x-axis?
What is the multiplicity is even.
300
vertical lines which correspond to the zeroes of the denominator of a rational function.
is it a vertical asymptote?
400
f(x + 3) Represents this type of transformation
Horizontal Shift 3 units Left
400
g(x) = 1/2(x-6)
What is 2x+6
400
The end behavior of f(x) = -log (x - 4)
As x -> -∞ , f(x) -> ∞
As x -> 4 , f(x) -> -∞
400
Write the function with roots -2,3,3
What is f(x) = (x+2)(x-3)^2
400
True Or False ?
horizontal asymptotes are horizontal curves that the graph of the function approaches as x tends to +∞ or −∞.
What is False ?
500
-f(x) and f(-x) Represents this type of transformation.
(Double points for specifying each!)
Reflections over the x - axis and y-axis (respectively)
500
f(x) =x2 +4
What is sq rt(x-4)
500
What is the end behavior of f(x) = 5x + 3
As x -> -∞ , f(x) -> 3
As x -> ∞ , f(x) -> ∞
500
2x^3+10x^2 +12x the roots are
What is 0,-2, -3
500
a line that a graph approaches more and more closely
what is an asymptote?