CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 10. Polar and Parametric Equations

x=t

y=t^2 +t− 4

The inverse is:

x=t^2 +t− 4

y=t

Concept Problem Revisited
The inverse of a function is not always a function. In order to see whether the inverse of a function will be a
function, you must perform the horizontal line test on the original function. If the function passes the horizontal
line test then the inverse will be a function. If the function does not pass the horizontal line test then the inverse
produces a relation rather than a function.

Vocabulary

Two functions are inversesif for every point(a,b)on the first function there exists a point(b,a)on the second
function.
Anintersectionfor two sets of parametric equations happens when the points exist at the samex,yandt.

Guided Practice

1. Find the points of intersection of the function and its inverse from Example C.


2. Does the point (-2, 6) live on the following function or its inverse?
   x=t^2 − 10
   y= 2 t− 4


3. Identify where the following parametric function intersects with its inverse.
   x= 4 t
   y=t^2 − 16