Review for Math 1410 Worksheet Name:
College Algebra
1. Draw a real number line and shade the following interval(s).
(a) [−2,∞)
(b) (−4,1/2)
(c) [−π/2,−1)
(d) (−∞,732)
(e) [0,2π]
(f) (−∞,∞)
2. Simplify
(a) 4a4
b5!2b3
a7
(b) 1
t+ 2 +t
t−1−3t
t2+t−2
(c)
1
y+y
y−1
2
y−1−1
y
(d) 3(x+ 5)
−1
4(x−2)2+ (x+ 5) 3
4(x−2)
3. Solve the following inequalities in terms of intervals and draw the solution set on a real number
line:
(a) 1 −7x≤3 + 4x
(b) | − 5x+ 3| ≤ 4
(c) x3−x2<0
(d) 0 <|x−5|<1/2
4. Draw a single coordinate plane and plot the following points
(a) (3,4)
(b) (−π, 1)
(c) (π, −1)
(d) (−1/2,−1/4)
5. State the formula for the distance between two points in the plane. Find the distance between
the points (2,5) and (4,−7).
6. Find the equation of the line through the following points.
(a) (0,3) and (2,1) (b) (−1,−1) and (1/2,3)
7. State any definition of a function y=f(x). State the definition of the domain of f(x).
8. State the Vertical Line Test (VLT).
9. State the definition of what it means for a function fto be increasing on an interval I. Repeat
for decreasing.
10. Sketch the following graphs (at most 2 graphs in a coordinate plane, please):
(a) y=x
(b) f(x) = x2
(c) g(x) = x3
(d) y=1
x
(e) y=|x|
(f) x2+y2= 4
(g) y=−x/2 + 4
(h) {(x, y)|x2+y2≤3}
(i) y= (x+ 3)2−1
11. Let f(x) = 3 −4x+x2−5x+1
3x−√x. Find the following, if possible:
(a) f(1)
(b) f(0)
(c) f(−1)
(d) f(a)
(e) f(a+h)
(f) f(x+h)
12. Let f(x) = √x. Let g(x) = x−19. Find (f◦g)(x), then state its domain.
13. Let f(x) = 1 −x9,g(x) = 1
x, and h(x) = cos x. Find the following compositions:
(a) (f◦g)(x)(b) (h◦f)(x) (c) (f◦g◦h)(x)
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