North Sydney Girls High School Mathematics and Equations Assignment

This document presents the solutions to a Mathematics and Equations assignment, likely for a high school level course. The assignment is divided into two activities, both involving the use of the Desmos graphing calculator. Activity 1 focuses on function analysis, including identifying asymptotes, marking intersections on a graph, determining the domain and range of functions, and understanding transformations. Activity 2 involves analyzing graphs of equations, describing shapes, and creating parametric curves using the Desmos platform. The student provides answers to questions, describes graphical features, and creates their own equations with adjustable parameters. The assignment covers a range of mathematical concepts, reinforcing understanding of functions, graphs, and equations.

Running head: MATHEMATICS AND EQUATIONS
Mathematics and Equations
Name of the Student:
Name of the University:
Author Note:

1MATHEMATICS AND EQUATIONS
Table of Contents
Activity 1: Class Code CKAJSB................................................................................................2
Activity 2: Class Code YZ5FH3................................................................................................3

2MATHEMATICS AND EQUATIONS
Activity 1: Class Code CKAJSB
# Question Answer Office Use
1 Observe the graph
2
Write the equations of the vertical
asymptotes y= −4
x2−4
3 Mark intersections On Desmos
4 Which is the graph of y f x = ( ) ? A
5 Observe the graph
6 Describe how to draw y=|f(x)| . On Desmos
7 Write down the domain of y = f (x)1/2 . - ∞ ≤ x ≥ + ∞
8 Write down the range of y =f (x)1/2. 4≤ y ≥ ∞
9 What transformation is this? A
10 What is the domain of f (x) g (x)? X>0 and x<0
11
For what values of x will the graph of f(x)*
g(x) be positive? 2 ≥ x
12 State a restriction on the domain X ≠ 2
13 Which is the graph of the inverse? B
14 Solve f(x) < g(x) ? X > -3
15 What is the value of f ( g (1)) ? 5
16 Solve g ( f ( x )) = 0 X = 2, 0

3MATHEMATICS AND EQUATIONS
17 Confirm and submit
Activity 2: Class Code YZ5FH3
# Question Answer Office Use
1
Observe the graph and answer
a to c
a
Describe the shape of the
graph when a = 1.
The graph shows a circle with radius 2
unit and the center is (0,0)
b
What is the Cartesian
equation of the graph when a
= 0 .
The graph shows a circle with radius of
1/2 unit and the center is (1,1)

4MATHEMATICS AND EQUATIONS
c
Draw the shape of the graph
when a = -3.
There are 4 ellipses that are connected at
(0,0). The description of 4 ellipses: 1)
with major axis on positive x-axis with
length of 2 units and the center is (1,0),
2) with major axis on positive y-axis
with length of 2 units and the center is
(0,1), 3) with major axis on negative x-
axis with length of 2 units and the center
is (-1,0) and 4) with major axis on
negative y-axis with length of 2 units
and the center is (0,-1).
2
Observe the graph and answer
a to c
a
Describe the effect of
changing the value of a.
With the fixed b=c=0, the circle moves
rightward on the x-axis with the
increasing value of a and the co-ordinate
of the center is (a,b).
b
Describe the effect of
changing the value of b.
With the fixed a=c=0, the circle moves
upward on the y-axis with the increasing
value of b and the co-ordinate of the
center is (a,b).
c
Describe the effect of
changing the value of c.
With the fixed a=b=0, the radius of the
circle increases with the increasing
value of c and the co-ordinate of the

5MATHEMATICS AND EQUATIONS
center for the specific case is (a,b) or
(0,0).
3 Create your own parametric curve
a
You must use a selection of the following to create your x and y
coordinates. Powers of t, such as 2 3 3 t t t t t , , , , ;Trig functions such as
sin ,cos , tan t t t ; Exponential functions such as 2 ,3 ,2 t t t - or other
functions studied in our course or combinations/compositions of these
Set your parameter values for t to range from -10 to 10
b
You must include one or more constants (a, b, c etc) in your equation.
For eg a t at t a sin ,sin ,sin + . Create sliders for any constants in your
equation, so that we can look at your graph for various values of a etc
c
Enter your parametric equations on Desmos. Leave the graph of your
parametric curve on the Desmos screen
d
Write down your parametric
equations here.
x=sin ( t2 +a ) +2bt
y=cos ( t2+ b ) +2at