MATH 1211 Unit 1 Written Assignment 2023/2024

1. What linear function, has and ?
Solution
f(0)=8 and f(7) = 14 implies that are two points on the line e.g (0, 8) and (7, 14)
finding the slope of the line between the two points employing
y 2− y 1
m= x 2−x 1
14−8
= 7−0
6
= 7

Using the slope at point (0, 8) in the point y – y1 = m(x – x1)
y – 8 = m(x - 0)
y = m(x - 0) + 8
y = mx + 8
f (x) = mx + 8
The graph is given below

2. If , what is ?
solution
(t +h ) + f (t)
finding f using f(t) = 2t – t2 + 3
h
2 t−t
= 2 (t +h )−( t+ h )2+ 3− (¿ ¿ 2+ 3)
h
¿
2 2 2
2 t+ 2h−t −2 th−h +3−2 t+ t −3
=
h
−h2+ 2 h−2 th
=
h

= - h – 2 + 2t
= - h + 2 – 2t


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, 3. Find all solutions to the equation . Write your answer
in radians in terms of
Solution
Given the equation
-4cosx = -sin2x + 1
Simplifying and rewriting the trigonometric identities
-4cosx = sin2x – 1= 0
1 – 2cos2x – 4cosx=0
Cos(x) = √ 6−2 /2 , cos(x)= -2 + √ 6−2 /2
For cos(x) = -2+ √ 6/2 there is no solution
For cos(x) = √ 6−2 /2 the possible solutions include
x = arccos ( √ 6−2 /2 ) + 2 π n
x = -arccos ( −√ 6−2 /2 ) + 2 π n
x = 1.79747 + 2 π n , x= -1.79747 + 2 π n

4. Sketch the graph of . Find the domain, range, and horizontal
asymptote. Include the horizontal asymptote in your graph

Solution




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