MAT1510 Assignment 2 (COMPLETE ANSWERS) 2024 (186115) - DUE 31 May 2024 ;100 % TRUSTED workings, explanations and solutions. For assistance call or W.h.a.t.s.a.p.p us on ...(.+.2.5.4.7.7.9.5.4.0.1.3.2)...........
ASSIGNMENT 02
Due date: Friday, 31 May 2024
Total Marks: 100
UNIQUE ASSIGNMENT N...
MAT1510
ASSIGNMENT 2 2024
UNIQUE NO. 186115
DUE DATE: 31 MAY 2024
, ASSIGNMENT 02
Due date: Friday, 31 May 2024
Total Marks: 100
UNIQUE ASSIGNMENT NUMBER: 186115
ONLY FOR YEAR MODULE
This assignment covers chapter 2 of the prescribed book as well as the study guide
DO NOT USE A CALCULATOR.
Question 1: 13 Marks
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give
an example that disproves the statement.
(1.1) If f is a function, then f (s + t) = f (s) + f (t). (3)
(1.2) If f (s) = f (t), then s = t. (2)
(1.3) If f is a function, then f (3x) = 3f (x). (3)
(1.4) A vertical line intersects the graph of a function at most once. (2)
1
(1.5) If f is one-to-one, then f − 1 (x) = . (3)
f (x)
Question 2: 9 Marks
The perimeter of a rectangle is 16 meters.
(2.1) If the length of one of the sides of the rectangle is (1 + x) meters, express the area A of the (4)
rectangle in terms of x.
(2.2) Calculate the maximum area of the rectangle. (3)
(2.3) What are the dimensions of the rectangle when its area is a maximum? (2)
Question 3: 6 Marks
Suppose a stone is thrown vertically upwards with a velocity ofu meters per second. Then its height is h (in
meters) after t seconds is given by the formula
h = ut − 4.8t 2 .
(3.1) Suppose the stone is thrown upwards with a velocity of 24 meters per second. Sketch the (5)
graph of the function defined by
h = ut − 4.8t 2 .
Label the axes properly, and show the coordinates of the critical points on the graph clearly.
16
, MAT1510/101/0/2023
(3.2) What is the maximum height that the stone reaches? (1)
Question 4: 6 Marks
Sketch the graph of the function g(x) which is piecewise-defined by
(4.1) (4)
− x 2 + 2x + 3 if x < 1
g(x) = 4 if x = 1
2
x − 2x + 5 if x > 1
(4.2) Explain why g is called a function. (1)
(4.3) Is g a one-to-one function? Give a reason for your answer. (1)
Question 5: 20 Marks
The sketch shows the graph of the functions f and g. Function f is defined by
y = f (x) = m|x − p| + q
17
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller LIBRARYpro. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R51,62. You're not tied to anything after your purchase.
