1. (i) Graph the function f(x) = 1
x
.
(ii) Hence, using translations and reflections etc., graph f(x) = 2 -
1
x - 3
. Make
sure you show and label the intermediate graphs.
2. When the domain for a given function is not specified, we adopt the convention
that the domain consists of all numbers for which the function is defined. Using
this convention, give the domain for the following functions and write your answers
using the interval notation. Be careful when considering the end points of each
interval.
(i) f(x) = 1 - x
v
x
2 - 4
(ii) f(x) = v
x
2 - x - 2.
3. Using calculus and showing all your working, find the following limits, if they exist.
(i) limx?2
2x
2 + 2x - 12
x - 2
(ii) limx?8
-3x
2 + x - 1, 000
2x
2 - 90
.
4. Consider the function defined by
f(x) =
?
?
?
x - 1 x
0 1 = x = 4
x - 2 x > 4.
Graph the function. Is the function continuous at x = 1 and x = 4? You should
justify your answer by addressing all the conditions for continuity.
5. Find the derivatives of the following functions
(i) f(x) = x
1/4 -
v
x(x
2 - 1)
(ii) y(x) = x
3 - 1
x
3 + 1
(iii) g(t) = [
(t
2 - 1)(t
3 + 2)]1/2
.
Notes:
• 10% of the marks for this assignment are reserved for presentation.
• There are penalties for late assignments. You must contact your tutor before the
due date if you have difficulties making the deadline
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Assignment 1 Due : 4pm Friday 17 August MAS182 Applied Mathematics Semester 2, 2012 Mathematics and Statistics 1 1. (i) Graph the function f(x) = . x 1 (ii) Hence, using translations and re?ections etc., graph f(x) = 2 . Make x3 sure you show and label the intermediate graphs. 2. When the domain for a given function is not speci?ed, we adopt the convention that the domain consists of all numbers for which the function is de?ned. Using this convention, give the domain for the following functions and write your answers using the interval notation. Be careful when considering the end points of each interval. 1x (i) f(x) = p 2 x 4 p 2 (ii) f(x) = x x2. 3. Using calculus and showing all your working, ?nd the following limits, if they exist. 2 2x +2x12 (i) lim x!2 x2 2 3x +x1;000 (ii) lim : 2 x!1 2x 90 4. Consider the function de?ned by ? x1 x <> 4: Graph the function. Is the function continuous at x = 1 and x = 4? You should justify your answer by addressing all the conditions for continuity. 5. Find the derivatives of the following functions p 1=4 2 (i) f(x) = x x(x 1) 3 x 1 (ii) y(x) = 3 x +1 [ ] 1=2 2 3 (iii) g(t) = (t 1)(t +2) . Notes: 10% of the marks for this assignment are reserved for presentation. There are penalties for late assignments. You must contact your tutor before the due date if you have di?culties making the deadline. 1