01-problems.pdf

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Artificial Neural Networks
Prof. Dr. Sen Cheng
Nov 02, 2020
Problem Set 1: Introduction
Tutors:
Eloy Parra (eloy.parra-barrero@ini.rub.de), Xiangshuai Zeng (xiangshuai.zeng@ini.ruhr-uni-bochum.de)
1.
Functions
In the following you find two relations,
f
and
g,
that map
x
onto
y.
Determine which one is a function and why.
(a)
f
:
x
→
y
such that
y
=
x
2
(b)
g
:
x
→
y
such that
y
2
=
x
Also, plot
y
vs.
x
for both relationships in Python and try to visually determine which one is a function. Note
that the range of
x
in your plot is limited and therefore you may not see the all of the characteristics of the
relationship, so choose the range carefully!
2.
Different types of functions
Plot the following functions for
x
∈
[−10,
10]. Be sure to plot them in a way that you can change the parameters
easily:
(a)
f
(x) =
0.5x
+
5
(b)
f
(x) =
5x
2
+
1x
+
100
(c)
f
(x) =
1x
3
+
1x
2
−
50x
+
100
(d)
f
(x) =
2e
−0.3x
Play out changing the values of the parameters. Can you tell what each parameter does? Try to describe how
the parameters in the linear and quadratic equations affect the result.
1

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