Practice Exam 3, Math 1111, Spring 2009
1. What is the domain of f(x) = √1−2x?Solution: (−∞,1
2])
2. What is the range of f(x) = |x−1|+ 2? Solution: [2,∞)
3. Describe how one can get the graph of y= 2(x+7)2from the graph of y= 2x2.Solution:
Moving to the left by 7.
4. Circle all the functions that are even.
5. Circle all the functions that are odd.
6. Suppose that the point (1,6) is on the graph of y=f(x). Find the point that must be
on the graph of y=f(x−4). Solution: (5,6)
7. Suppose that the point (1,6) is on the graph of y=f(x). Find the point that must be
on the graph of y=−2f(x). Solution: (1,−12)
8. Let f(x) = 2x2−3xand g(x) = 4x−3. Find (f◦g)(0). Solution: 27
9. Let f(x) = 2x2−3xand g(x) = 4x−3. Find (f−g)(1). Solution: −2
10. Let f(x) = 2x2−3xand g(x) = 4x−3. Find (fg)(2). Solution: 10
11. Let f(x) = x
2x+1 and g(x) = 4x−3. Find (f◦g)(x). Solution: (f◦g)(x) = 4x−3
8x−5
12. Find the vertex of y=−x2+x−1
4.Solution: ¡1
2,0¢
13. Find the range of y=−x2+x−1
4.Solution: (−∞,0]
14. Find the correct pair of the axis of symmetry and shape of y=−x2+x−1
4.Solution:
x=1
2, open downward.
15. Find the quadratic function that has its vertex (1,2) and passing through (0,5). Solu-
tion: y= 3(x−1)2+ 2
16. Find the quotient when x3−4x2+ 9x−6 is divided by x−1. Solution: x2−3x+ 6
17. Find the remainder when x4+x2−3x+ 1 is divided by x+ 1. Solution: 6
18. Find all the solutions of x3+ 2x2−3 = 0. Solution: 1,−3+√3i
2,−3−√3i
2
19. Find the cubic polynomial function f(x) that has zeros 1 and 3 and −2 such that
f(0) = 4. Solution: f(x) = 2
3(x−1)(x−3)(x+ 2).
20. Among the alternatives, find all possible rational zeros of f(x) = 2x3+a2x2+a1x−6
for integers a2and a1.Solution: ±1,±2,±3,±6,±1
2,±3
2
21. Describe how one can get the graph of y=1
xfrom the graph of y=1
x−1. Solution:
Moving up by 1.
1