Practice Exam 3
Name:
Instructions:
Give yourself 50 minutes to complete this practice exam.
Justify each answer.
1.
11.
2.
12.
3.
13.
4.
14.
5.
15.
6.
16.
7.
17.
8.
18.
9.
19.
10.
20.
21.
22. p(x)
−7 −6 −5 −4 −3 −2 −1
0
1
2
3
4
5
6
7
−7 −6 −5 −4 −3 −2 −1
0
1
2
3
4
5
6
7
23. r(x)
26. e−(x+2)
24. ex
4
3
2
1
−4 −3 −2 −1
−1
1
2
3
4
1
2
3
4
−2
−3
−4
27. −loge (x) − 1
25. loge (x)
4
3
2
1
−4 −3 −2 −1
−1
−2
−3
−4
28. r(x)
−7 −6 −5 −4 −3 −2 −1
0
1
2
3
4
5
6
7
True or False
For # 1-6, completely write either, ”True,” or, ”False.”
1. ax ay = axy
2. (ax )y = ax+y
3.
ax
ay
= ax−y
4. loga (z + w) = loga (z) + loga (w)
5. loga (z w ) = w loga (z)
6.
loga (z)
loga (w)
= loga (z) − loga (w)
3
40
7. Write (10 10 ) 3 as a rational number in standard form.
8. Write
16
9
− 12
as a rational number in standard form.
9. Write 6129 6−134 63 as a rational number in standard form.
3
10. Write 25 2 as a rational number in standard form.
11. Write log10 (1, 000, 000) as a rational number in standard form.
√
12. Write log3 ( 2 27) as a rational number in standard form.
13. Which is the greatest integer that is less than log2 (100)?
14. Solve for x: ex = 15.
15. Solve for x: loge (x) = 6.
16. Solve for x: ex + 2 = 10.
17. Solve for x: loge (x − 3) = −1.
18. Solve for x: e2x = ex+1 e2 .
19. Solve for x: log2 (x + 4) + log2 (x) = 2.
20. Find a root of x3 − 2x2 − 2x − 3.
21. Completely factor 5x3 − 9x2 + 8x − 20. (Hint: 2 is a root.)
Graphing
22. Graph
p(x) = −(x + 3)(x − 6)(x − 6)(x2 + 2)
23. Graph
r(x) =
9(x − 1)(x + 2)
5(x − 3)(x2 + 2x + 8)
24. Graph ex and label its y-intercept. (This means you should mark that point and
write its coordinates down.)
25. Graph loge (x) and label its x-intercept.
26. Graph e−(x+2) and label its x- or y−intercepts (if there are any.)
27. Graph − log10 (x) − 1 and label its x- or y−intercepts (if there are any.)
28. Extra Credit Graph
r(x) =
(x + 1)(x + 3)
(x + 4)(x + 3)