Math1210-001 Weekly Assignment 1
Spring, 2016
(Algebra/function Review, 1.1, 1.3)
instructor:
Uid number:
name:
Instructions: Please show all of your work and explain your reasoning, as partial credit will
be given where appropriate, and there may be no credit given for problems where there is
no work shown. All answers should be completely simplified, unless otherwise stated.
(Total of 100 points possible.)
1. Factor each expression completely
(a) (5 points) 2x2 − 50
Answer:
(b) (5 points) x3 + 125
Answer:
(c) (5 points) 6x2 + 7x − 20
Answer:
(d) (5 points) x3 − 3x + 2
Answer:
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2. Simplify these expressions, writing your answer in exponent form with only positive
exponents.
2 −2 −2
xw
(a) (5 points)
4−1 x5 w
Answer:
v
u 1√
u y 2 yp
4
p
(b) (5 points) t
3
p2
Answer:
3. Given the functions f (x) =
p
5
1
(x + 3), g(x) = + 1 and h(x) = √ , find the following.
x
x
(a) (4 points) g −1 (x)
Answer:
(b) (4 points) f (w − 1)
Answer:
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(c) (4 points)
g(y + h) − g(y)
h
Answer:
(d) (4 points) f (g(h(x)))
Answer:
(e) (4 points) g(g(x))
Answer:
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4. Find each of these limits or state that the limit does not exist and explain why not.
x2 − 16
(a) (8 points) lim √
x→4
x−2
Answer:
−x3 + 10x
x→0 x2 − 3x + 2
(b) (7 points) lim
Answer:
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5. (8 points) For the function f (x) and its graph, of y = f (x), shown below, answer the
following questions. Write DNE (short for ”does not exist”), if the limit or function
value does not exist, and explain why it does not exist.
(a) lim f (x) =
(e) f (2) =
x→0
(b) lim− f (x) =
(f) f (0) =
(c) lim+ f (x) =
(g) lim− f (x) =
x→2
x→2
x→2
(d) lim f (x) =
(h) f (π) =
x→2
6. (7 points) Find a piecewise-definition for the function whose graph is displayed in the
previous problem. In other words, identify sub-intervals of the real line domain, and
algebraic function formulas for how to compute the function values on those
subintervals.
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7. (10 points) Create a piecewise-defined function (algebraically), whose domain is all real
numbers, and so that all four of the function values and limit statements below are
true. In other words, you have decide on formulas for f (x) for appriate subintervals or
points of the real line. Note that there are many possibilities. (The problem after this
one asks you to sketch the graph of your creation. You may want to think about both
problems simultaneously.)
(a) lim+ f (x) = 3
x→1
(b) lim− f (x) = 5
x→1
(c) lim f (x) = 2
x→−2
(d) f (−2) = −1
8. ( 10 points ) Sketch the graph of the function you created in the previous problem.
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