CK-12-Pre-Calculus Concepts

10.4. Parametric Inverses http://www.ck12.org

x= 4 ( 2 + 2 √ 5 ),y= ( 2 + 2 √ 5 )^2 − 16

x= 4 ( 2 − 2

√

5 ),y= ( 2 − 2

√

5 )^2 − 16

Practice

Use the functionx=t−4;y=t^2 +2 for #1 - #3.

1. Find the inverse of the function.


2. Does the point (-2, 6) live on the function or its inverse?


3. Does the point (0, 1) live on the function or its inverse?
   Use the relationx=t^2 ;y= 4 −tfor #4 - #6.


4. Find the inverse of the relation.


5. Does the point (4, 0) live on the relation or its inverse?


6. Does the point (0, 4) live on the relation or its inverse?
   Use the functionx= 2 t+1;y=t^2 −3 for #7 - #9.


7. Find the inverse of the function.


8. Does the point (1, 5) live on the function or its inverse?


9. Does the point (9, 13) live on the function or its inverse?
   Use the functionx= 3 t+14;y=t^2 − 2 tfor #10 - #11.


10. Find the inverse of the function.


11. Identify where the parametric function intersects with its inverse.
    Use the relation x=t^2 ;y= 4 t−4 for #12 - #13.


12. Find the inverse of the relation.


13. Identify where the relation intersects with its inverse.


14. Parameterizef(x) =x^2 +x−6 and then graph the function and its inverse.


15. Parameterizef(x) =x^2 + 3 x+2 and then graph the function and its inverse.