Section 1: Insights from Dictionary of Engineering Functions: Name:______Student ID:______

Q1 (insights from Task 1). Examine the graphs you have drawn for in Task 1 and fill in the table given:

Linear / Quadratic / Cubic / Quartic
What is the maximum number of times the graphs can cross the X-axis?
What is the maximum number of turning points the graphs can have?

Q2 (insights from Task 2). Examine the graphs you have drawn in Task 2 and fill in the following table to comment on the general shape and similarity of the graphs.

Function / General shape / Similarity
f(x) and h(x)
g(x) and m(x)
p(x), q(x) and r(x)

Q3 (insights from Task 3). Examine the graphs you have drawn in Task 3 and fill in the following table to comment on the general shape and similarity of the graphs.

Function / General shape / Similarity
f(x) and m(x)
f(x) and p(x)
f(x) and q(x)


Section 2: Insights from exploring families of functions using parameters via GeoGera applets.

Name:______Student ID:______

In the exercises in section 2 you will use GeoGebra Applets provided to investigate the effects on a given family of engineering function of adjusting parameters within that function.

Note: the applets work best in Google Chrome.

Note: that each Geogebra applet has a RESET button.

Q4. To investigate the effects of changing A and k in the ‘cistern’ function f(t) =A(1 – e-kt)

The GeoGebra applet Cistern_function on the course Moodle page is designed to investigate the effects of changing the parameters A and k in f(t) =A( 1 – e-kt ).

Write a short comment on the effect of changing the parameter k in the exponential function has on the graph of

f(t) =A( 1 – e-kt ).

Write a short comment on the effect of changing the parameter A in the exponential function has on the graph of

f(t) =A( 1 – e-kt )


Q5. To investigate the effects of changing A and w in the basic trigonometric functions

f(x) = Asin(wx) and g(x) = Acos(wx).

The GeoGebra applet TrigWavesBasic on the course Moodle page is designed to investigate the effects of changing the parameters A and w in f(x) = Asin(wx) and g(x) = Acos(wx).

Write a short comment on the effect of changing the parameter A has on the graphs of

f(x) = Asin(wx) and g(x) = Acos(wx).

Write a short comment on the effect of changing the parameter w has on the graphs of

f(x) = Asin(wx) and g(x) = Acos(wx).

Q6 To investigate the translational effects on a given function of adjusting parameters within that function.

(a)  The GeoGebra applet MovingQuads on the course Moodle page is designed to enable you to investigate the effects of changing the parameters A, B, d and V in f(x) = A( B(x + d) )2 + V on the quadratic function g(x) = x2

Using this tool complete the table given below with comments on the relationship between the graph g(x) = x2 and the graphs of the other given functions. In each case note a ‘key’ point on the graph.

Comment / Key point
g(x) = x2 / Original graph / (0,0)
(i) / f(x) = (x + 5)2
(ii) / f(x) = (x -3)2
(iii) / f(x) = x2+4
(iv) / f(x) = x2-3
(v) / f(x) = (x + 5)2 -2
(vi) / f(x) = 4(x +2)2
(vii) / f(x)= -9(x-3)2

Complete the table below to summarise the effect changing the listed parameters has on the graph of the function relative to the graph f(x) = x2.

Comment
A
d
V

Q6(b) The GeoGebra applet MoveLn on the course Moodle page is designed to enable you to investigate the effects of changing the parameters A, B, d and V in f(x) = A ln(k (x + d)) + V on the natural log function f(x) = ln(x)

Using this tool complete the table given below with comments on the relationship between the graph f(x) = ln(x) and the graphs of the other given functions:

Comment / Key point
g(x) = ln(x) / Original graph / (1,0)
(i) / f(x) = ln(x-3)
(ii) / f(x) = ln(x+4)-3
(iii) / f(x) = ln(x-2)-3

Complete the table below to summarise the effect changing the listed parameters has on the graph of the function relative to the graph g(x) = ln(x).

Comment
d
V

Q6(c)The GeoGebra applet TrigWavesmoving on the course Moodle page is designed to enable you to investigate the effects of changing the parameters A, w, d and V in f(x) = A sin(w (x + d)) + V on g(x) = Asin(wx)

Using this tool complete the table given below with comments on the relationship between the graph of

g(x) = Asin(wx) and the graphs of the other given functions:

Comment / Key point / Ampliude / Period
g(x) = Asin(wx) / Original graph / (0,0) / A / 6.28/w
(i) / f(x) = 4sin(x)+3
(ii) / f(x) = 2sin(x- 3)
(iii) / f(x) = 2sin(3(x+1))
(iv) / f(x) = 5sin(3x- 6)
(v) / f(x) = 5sin(3x- 6)+1

Complete the table below to summarise the effect changing the listed parameters has on the graph of the function relative to the graph f g(x) = Asin(wx)

Comment
d
V