Math 125 Practice Test #4 (Chapter 10 and Chapter 11) Find the Equation of the Line Satisfying
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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 6x+ 3 y = 5 2. Through (-4,5) ; perpendicular to 2x- 3 y = 6 3. Through (4,0) and (-4, - 5)
Graph the following piecewise function. Use the graph to determine the domain and range. 4x- 4 if x < 2 4. f( x ) = -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 p2 .
7. The volume of a cone varies jointly as its height and the square of its radius. If the volume of a cone is 32p in3 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. 2 8. f( x )=( x - 1) + 3 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
-3x + 4 13. 5x - 2� 2 or 5x - 2 > 2 14. -6＃ 8 2
15. 3x + 1 > 10 16. 2x - 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. 2x - 1 = 5 20. 10- 2y = 4 y - 3
Graph the inequality or system of inequalities. x5 y 21. 2x- 4 y < 12 22. x+4 y > 4
______Answer key in on the next page. Answer key:
1) f( x )= - 2 x - 2
3 2) f( x )= - x - 1 2
5 5 3) f( x ) = 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 =( -ゥ , ) ; Range =( - ,4)
5) a)f (0)= - 4, b) f (2) = - 1, c) f (4) = - 3, and d) x = 3
kx 6) y = p2 7) 15p in3
8) a) Start with x2 , shift right 1, then shift up 3 (Blue graph is x2 , Red graph is (x - 1)2 + 3) b) Domain =( -ゥ , ) ; Range = (3, )
9) a) Start with x , reflect across y-axis, then shift down 4 (Blue graph is x , Red graph is -x - 4 ) b) Domain =( - ,0) ; Range =( - 4, )
x 4 y 10
5
x 10 5 5 10
5
10 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 =( -ゥ , ) ; Range =( - , 5) y 10
5
x 10 5 5 10
5
10
4 4 11.) x 4 ; (4,) 12.) x 1 and x ; 1, 3 3
4 4 16 16 13.) x 0 or x ; (,0] , 14.) 4 x ; 4, 5 5 3 3
11 骣 11 15.) x 3 or x ; 琪-ト,( 3, ) 16.) 5 x 6 ; (-5,6) 3 桫 3
17.) A B {3,2,1,0,1, 2,3, 4,10} 18.) A B {2, 2}
13 7 19.) x 3; x 2 20.) x ; x 6 2
21.) 22.)