What is a one-to-one function?
A one-to-one function is one in which each input (number that replaces the variable)
has exactly one output (result of the equation). In such cases, the function needs to
pass the “horizontal line test,” showing that a horizontal line intersects the graph once
and only once. For example, for the equation f(x) x^2 , if one restricts the answer to x≥
0, the result is a one-to-one function; but the equation with no constraints is not a one-
to-one function, as the output value of 4 has the two input values of 2 and 2.What is the definition of a conic section?
This family of curves—first discovered (as far as we know) by the ancient Greeks—is
generated by planes intersecting (“cutting into”) a cone. The resulting feature depends
on the angle between the plane and the axis of the cone, with none of the planes pass-
ing through the endpoint (vertex) of the cone. Each plane that cuts a cone creates a
two dimensional figure called a section,thus the resulting figures are called conic sec-
tionsor conics. In general, the possible resulting surfaces are a sphere (the cut per-
pendicular to the axis), ellipse (or the circle as a special case; a cut moderately
inclined to the axis), parabola (a cut parallel to one of the straight lines that generate
the cone), and hyperbola (using two cones tip to tip, the cut even more steeply
inclined than all the others).What are polar coordinates?
Polar coordinates are actually an alternative system to the Cartesian coordinates. In
198 two dimensions, they mark a point on a plane by its radial distance (r) from an “ori-
Depending on the way a plane intersects a cone shape, different types of curves will be the result.