MATH 4C HW #4
Book Problems
2.4: 26, 28
3.2: 26, 28, 30
3.3: 16, 22
Other Problems
1) Classify the following as polynomials, rational functions, or neither.
1
x4
(d) f (x) =
(a) f (x) = x4 −3x−10 (b) f (x) = x4 −3x 2 −10 (c) f (x) = 3x−10
(e) f (x) = 18
2x
3x +1
2) Give an example of polynomials p and q of degree 5 such that deg(p+q) does
not equal 5.
3) Divide 3x4 + x2 + 2 by x2 + 1.
4) Let f (x) = x4 + 5x3 + 5x2 − 5x − 6
(a) Find f (1) and f (−1)
(b) Solve f (x) = 0 (Hint: Use (a))
Graph the following, write any intercepts, and draw and label any asymptotes and holes.
Show all steps
5) y =
2x2 + 5
x2 − 25
6) y = 1 − 23−x
7) y =
x2 + 3x
x3 + 3x2 − x − 3
8) y = − log2 (−4 − x) − 2
9) y = 5 + |3−x − 1|
−3x2 + 3 10) y = 2
x + 2x + 1 Simplify
1
11) (a) log( 10
) (b) log4 ( 18 )
12) (a) log3 (−9) (b) log3 (0)
√
√
13) (a) log32 ( 2) (b) log 1 ( 5 27)
9
√ π
14) (a) log8 (( 2) ) (b) log 1 (4) log4 (81)
3
15) (a)
1
1
ln( 36
)
ln( 36
)
(b)
√
ln(6)
log e (6)
1
16) (a) ln(4e) + ln( 4e
) (b) log5 (25 − 5) − log5 (100) (c) ln
Solve
17) 3x =
1
27
18) 34+x = 6
19) ln(x) =
1
8
20) log4 (x2 − x) = 2
21) 53+2x = 5x
2 +6
22) 52x − 5(5x ) = 36
23) 22x + 2x+1 − 24 = 0
24) (ln(x))4 > 2(ln(x4 ))
25) log3 (x − 1) + log3 (2x − 5) = 2.
2
26) log4 ( 4−7x
)=
x−5
3
2
27) log4 (4 − 7x2 ) − log4 (x − 5) =
3
2
28) log2 (x) + log4 (x) + log8 (x) = 11
29) log3 (x) − 8 logx (3) = −2
x
30) log2 (4x) log2 ( 32
)=8
31) e3x + 9e2x − 9ex − 1 ≤ 0
Find the domain
32) f (x) = log3 (4x − 20)
4 33) f (x) = log3 xx3 −1
+1
34) f (x) = log3
x4 −13x2 +36
x2 +x−6
35) f (x) = ln(ln(ln(x)))
p √
e e