Functions – Precalculus
Evaluate.
1. Find the following values for the function f ( z )  3z  4 .
(a) f (2)
(b) f (3)
(c) f ( z  3)
(d) f (4 z )
(e) f ( z  q)
2. If f  x   x 2  x  6 , then find f  5 .
3. If f  x   x 2  2 x  5 , then find f  3a  .
4. If f  x   2 x 2  3x  6 , then find f  a  h  .
5. If f  x   3x  20 , what value of x does f  x   4 ?
6. If g  x   5 x  19  20 , what value of x does g  x   27 ?
3
7. If h  x   2 x  19 , what value of x does h  x   231 ?
Graph using transformation techniques.
8. Use the graph of y  f ( x) to graph the function g 
1
f  x .
2
9. The graph of y  f ( x) is shown in the figure below. Graph the function y  f  2 x  .
10. The graph of y  f ( x) is shown in the figure below. Graph the function y   f   x  .
11. The graph of y  f ( x) is shown in the figure below. Graph the function y  f ( x) .
Find the domain.
12. Find the domain of f ( x) 
x 5
. Write it in interval notation.
x2
Determine each relation or graph if it is a function, give the domain and range, and evaluate.
13. (a) Determine if the relation { 2, 2  ,  3, 0  , 1, 4  ,  9,5  ,  6, 4  ,  7,8 } is also a function.
(b) Give the domain and range of the relation of { 2, 2  ,  3, 0  , 1, 4  ,  9,5  ,  6, 4  ,  7,8 } .
14. (a) Determine whether the graph illustrated represents a function.
(b) Give the domain and range of each function or relation in
interval notations.
(c) Approximate the value or values of x where y  2 .
15. (a) Determine whether the graph illustrated represents a function.
(b) Give the domain and range of each function or relation in
interval notations.
(c) Approximate the value or values of x where y  2 .
16. (a) Determine whether the graph illustrated represents a one-to one function.
(b) Give the domain and range of each function or relation in interval
notations.
(c) Approximate the value or values of x where y  2 .
(d) Does f 1  x  exist?
Evaluate the composite functions.
17. If f  x   2 x 2  7 x  4 and g  x   4 x , find
f
g  1 .
18. If f  x   2 x and h  x   x , find g  h  2   .
19. If f  x   5x 2  12 x  8 and g  x   2 x , find (a)  f g  x  and (b)  g f  x  .
Graph the functions.
20. Graph the piecewise-defined function.
if x  1
 x

f  x  
2 x  2 if x  1

21. Graph the piecewise-defined function.
3 if x  2

g  x  
5 if x  2

Find the equations of the circle.
22. Write the standard form of the equation of the circle with center  3, 4  and radius 5 .
23. Write the standard form of the equation of the circle with center  1, 5 and radius
5.
Answer key
1. (a) 2 (b) 13 (c) 3 z  13 (d) 12 z  4 (e) 3z  3q  4
2. 14
3. 9a2  6a  5
4. 2a2  4ah  2h  3a  3h  6
5. x  12
6. x  6
7. x  5
8.
9.
10.
11.
12. D   , 2    2,  
13. a) Yes b) D  {2,3,1,9,6,7} ; R  {2,0, 4,5, 4,8}
14. a) Yes b) D   ,   , R   ,   ; c) x  3
15. (a) Yes (b) D   ,   , R   0,   (c) x  3, 5
16. (a) No (b) D   2, 2 , R   5, 2 (c) x  2, 2 (d) No
17. 56
18. 2 2
19. (a) 10 x  12 2 x  8 ; (b) f  x   10 x 2  24 x  16
20. d)
21. c)
22.  x  3   y  4  25
2
2
23.  x  1   y  5  5
2
2