CK-12-Pre-Calculus Concepts

1.11. Function Composition http://www.ck12.org

Practice

For questions 1-9, use the following three functions:f(x) =|x|,h(x) =−x,g(x) = (x− 2 )^2 −3.

1. Graphf(x),h(x)andg(x).


2. Findf(g(x))algebraically.


3. Graphf(g(x))and describe the transformation.


4. Findg(f(x))algebraically.


5. Graphg(f(x))and describe the transformation.


6. Findh(g(x))algebraically.


7. Graphh(g(x))and describe the transformation.


8. Findg(h(x))algebraically.


9. Graphg(h(x))and describe the transformation.
   For 10-16, use the following three functions:j(x) =x^2 ,k(x) =|x|,m(x) =√x.


10. Graphj(x),k(x)andm(x).


11. Findj(k(x))algebraically.


12. Graphj(k(x))and describe the transformation.


13. Findk(m(x))algebraically.


14. Graphk(m(x))and describe the transformation.


15. Findm(k(x))algebraically.


16. Graphm(k(x))and describe the transformation.