Mathematics and Equations

This document provides study material on mathematics and equations. It covers topics such as graphing, equations of asymptotes, domain and range, transformations, and more.

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