Math 125 Practice Test #4 (Chapter 10 and Chapter 11)
Find the equation of the line satisfying the given conditions. Write the answer using
function notation.
1.
Through  2, 6  ; parallel to 6 x  3 y  5
2.
Through  4,5 ; perpendicular to 2 x  3 y  6
3.
Through  4, 0  and  4, 5
Graph the following piecewise function. Use the graph to determine the domain and range.
4 x  4 if x  2
f ( x)  
4.
  x  1 if x  2
5. For the piecewise function f ( x) in question 4, a) find f (0) ; b) find f (2) ; c) find f (4) ;
and d) use the graph to find x such that f ( x)  2 .
6. Write an equation to describe the variation: y varies directly as x and inversely as p 2 .
7. The volume of a cone varies jointly as its height and the square of its radius. If the
volume of a cone is 32 in 3 when the radius is 4 in and the height is 6 in , find the
volume of a cone when the radius is 3 in and the height is 5 in.
For each of the following functions,
a) determine the transformations (shift up, down, left, right, reflect,....).
b) determine the domain and range.
8.
f ( x)   x  1  3
2
9. g ( x)   x  4
10. h( x)   x  3  5
Solve , graph, and write in interval notation for each inequality.
11. 3  2x  5
12. x  1  0 and 3x  4  0
13. 5x  2  2 or 5x  2  2
15.
3x  1  10
14. 6 
16.
3 x  4
8
2
2 x 1  4  15
Given A  2,0, 2, 4,10 and B  3, 2, 1, 1, 2, 3
17. Find A  B
18. Find A  B
Solve the given equations.
19. 2 x 1  5
20. 10  2 y  4 y  3
Graph the inequality or system of inequalities.
21. 2 x  4 y  12
 x  5y
22. 
x  4 y  4
______________________________________________________________________________
Answer key in on the next page.
Answer key:
1)
f ( x)  2 x  2
2)
3
f ( x)   x  1
2
3)
f ( x) 
5
5
x
8
2
4)
5
4
3
2
1
3
2
1
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
9
10
Domain  ( ,  ) ; Range  ( , 4)
5) a) f (0)  4,
6)
y
kx
p2
b) f (2)  1, c) f (4)  3, and d) x  3
7) 15 in 3
2
2
8) a) Start with x , shift right 1, then shift up 3 (Blue graph is x , Red graph is ( x  1) 2  3 )
b) Domain  ( ,  ) ; Range  (3, )
9) a) Start with
x , reflect across y-axis, then shift down 4 (Blue graph is
x  4 )
b) Domain  ( , 0) ; Range  ( 4, )
x
4
y
10
5
10
5
5
5
10
10
x
x , Red graph is
10) a) Start with x , shift left 3, reflect across the x-axis, then shift up 5 (Blue graph is x ,
Red graph is  x  3  5 )
b) Domain  ( ,  ) ; Range  ( , 5)
y
10
5
10
5
5
10
x
5
10
11.) x  4 ; (4, )
13.) x  0 or x 
4
4 
; ( ,0]   ,  
5
5 
 11 
11 
;  ,    3,  
3
3

17.) A  B  {3,2,1, 0,1, 2, 3, 4,10}
15.) x  3 or x 
12.)
x  1 and x 
14.)
4 x
16
;
3
4
;
3
4

  1, 
3

16 

 4, 3 
 5, 6 
16.)
5  x  6 ;
18.)
A  B  {2, 2}
19.) x  3; x  2
20.)
x
21.)
22.)
13
7
;x
6
2