Math 123C Reyes
Review Test 2: Functions & Transformations (Chapters 6, 10, & 9)
Graph paper is provided at the end.
1. Find the domain and range of the relation:
 5,8, 4,8, 7,8
2. Determine if the given relation is also a function:
 2,1,  2,4, 2,9
3. Use the vertical line test to determine whether the given graph is the graph of a function.
4. Given the function f ( x)  x  10 , find each of the following: f (10), f  7, f 0
5. Find the domain of the given function: h( x) 
1
x7
6. Find the domain and range of the graphed function:
7. Forensic scientists use the following function to find the height of a woman if they are given the
height of her femur bone f, in centimeters. Find the height of a woman whose femur measures 51 cm:
H ( f )  2.59 f  47.24
2
8. Given the function f ( x)  x  8 , find f (8) and f (a )
9. Graph the linear equation:
f ( x)  3x  3
10. Graph the linear equation:
2
f ( x)   x
3
11. Find an equation of the line with the given slope and containing the given point. Write the equation
using function notation: slope 7: through (5, 3)
12. Find an equation of the line passing through the given points. Use function notation to write the
equation. (4, 6) and (6,12)
13. Write the equation of the line using function notation. Horizontal; through (0, -3)
14. Find an equation of the line. Write the equation using function notation. Through 2,4 ;
perpendicular to 8 y  x  16
15. Find an equation of the line. Write the equation using function notation. Through  4,8 ; parallel
to 5 x  4 y  9 .
16. Use the graph of the function shown to find all positive values of x such that g(x) = 8.
17. Graph the piecewise-defined function. Then state the domain and range.
 x  2 if x  1
f ( x)  
 2 x  2 if x  1
 2 if x  0
 8 if x  1
18. Graph the piecewise-defined function. Then state the domain and range. g ( x)  
19. Sketch the graph of the function. f ( x) 
x  3 1
20. Sketch the graph of the function. g ( x)   x  3
2
21. Sketch the graph of the function. g ( x)   x  2  4
22. Sketch the graph of the quadratic function. f ( x)  x  2  7 . Sketch the axis of symmetry. State
the vertex, and give the equation for the axis of symmetry.
2
23. Sketch the graph of the quadratic function. h( x)  4 x  10  2 . Sketch the axis of symmetry.
State the vertex, and give the equation for the axis of symmetry.
2
24. Use the graph of y  f (x) to graph the function y  f ( x  4)  1
25. Find the vertex of the graph of the quadratic function. Determine whether the graph opens upward
or downward, find any intercepts, and sketch the graph. f ( x)   x 2  8x  7
26. Find the vertex of the graph of the quadratic function. Determine whether the graph opens upward
or downward, find any intercepts, and sketch the graph. f ( x)  25 x 2  30 x  8
27. Find the vertex of the graph of the quadratic function. Determine whether the graph opens upward
or downward, find any intercepts, and sketch the graph. f ( x)  6 x 2  6 x
28. If a baseball is projected upward from ground level with an initial velocity of 32 feet per second, then
its height is a function of time, given by s  16t 2  32t . What is the maximum height reached by the
ball?
29. The cost C in dollars of manufacturing x bicycles at a production plant is given by the function
C ( x)  5 x 2  1000 x  62,000 .
a) Find the number of bicycles that must be manufactured to minimize the cost.
b) Find the minimum cost.
Graph paper: