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
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