Functions Worksheet - Math 121: Extra Practice For Test 2 Page 5
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2
3
4
514. Following the steps given above, sketch the graph of the given rational functions:
2
2x
+ 2x
12
(a) f (x) =
2
x
x
6
4
x
(e) f (x) =
2
3
x
9
x
(b) f (x) =
2
x
4
2
x
9
(f) f (x) =
3
3x
2
x
2x
3
(c) f (x) =
2
(x
1)
2
(x + 2)(x
2x + 1)
(g) f (x) =
2
(x
1)
2
x
+ 5x + 6
(d) f (x) =
2
x
1
15. Make up a function that fits the listed conditions:
(a) A function whose domain is all reals except 3.
(b) A function whose range is everything except 0.
(c) A function whose graph has vertical asymptotes at 2 and 5 and a horizontal asymptote at 1.
(d) A function whose graph has a horizontal asymptote at y = 0 and no vertical asymptotes.
5
Inequalities
16. Solve the given inequalities. Represent your solution, using interval notation.
x + 1
2
(a) x
< x
(k)
0
x(x + 3)
2
(b) x
+ 1
0
6
(l)
0
x + 3
2
(c) x
+ 2x
1
6
(m)
1
x + 3
(d) x + 5
5 < 7
6
(e) 2 7
x + 1 > 4
(n)
< 1
x + 3
2
(f) x
3
2x
2
x
8x + 12
(o)
< 0
2
x
16
2
(g) 5x + 4
3x
6
(p)
0
2
x
+ 3
2
(h) 5x + 4 < 3x
3x
1
11
15
(q)
1
(i)
x
3
2
x
+ 1
4
4
(x
2)(x
1)
2x + 17
(j)
0
(r)
x + 5
x + 3
x + 1
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