Curves From Geometry
A line that continually approaches a given curve but never touches it.
Asymptote
Cavalieri's Principle is based on the...
cross-sectional areas.
A rational function is a function made up of a ratio of...
polynomials.
The domain is.....
The range is.....
x-values, y-values.
a composite function is a function that depends on...
another function
the set of all points where the difference in the distance from two fixed points (foci) is constant.
Hyperbola
Slicing a cone will you give one or all of these.
Circle, ellipse, parabola, or hyperbola
f(x)= p(x)/?
q(x), where q(x) cannot equal 0.
asymptotes are usually....
dashed lines
given f(x)=x2 and g(x)= x+5, what is f(g(x))?
f(g(x))=(x+5)2
x2 + y2 = 1 is the...
Standard ellipse equation
r2= R2 - ?
x2
given f(x) = (2x-1)/(x-4), state the domain.
x=4, so all real numbers except when x=4.
given f(x)=x2 and g(x)= x+5, what is f(g(4))?
81
A curved line forming a closed loop, where the sum of the distances from two points (foci) to every point on the line is constant.
Ellipse
Let R = 5, what is A(1)?
24pi
Given f(x)=x, what is the end behavior?
as x -> positive or negative infinity, f(x) -> approaches positive or negative infinity
given f(x) = (2x-1)/(x-4), state the end behavior of f.
(2x)/x= 2, so as x approaches negative or positive infinity, the function approaches 2.
given f(x)=x2 and g(x)= x+5, what is g(g(x))?
(x+5) +5.
WHat is the symmetry of an ellipse, an up/down hyperbola, and a left/right hyperbola?
about the center, about the y-axis, and about the x-axis.
Let R=5, what is B(3)?
16pi
determine the end behavior of f(x) = (x2-3)/(x3)
1/x. So as x approaches positive or negative infinity, f(x) approaches 0.
given f(x) = (2x-1)/(x-4), state the horizontal asymptote.
y=2
given f(x)=x2 and g(x)= x+5, what is f(f(x))?
x4